Go through the Spectrum Math Grade 6 Answer Key Chapter 1 Lesson 1.8 Least Common Multiple and get the proper assistance needed during your homework.
Spectrum Math Grade 6 Chapter 1 Lesson 1.8 Least Common Multiple Answers Key
Find the least common multiple by listing multiples of each number until finding the first one that is shared.
Find the least common multiple for each set of numbers.
Question 1.
a. 51 and 18 _____________
Answer:
Least common multiple of 51 and 18: 306.
Explanation:
Multiples of 51:
51,153, 204, 255, 306, 357, 408, 459, 510.
Multiples of 18:
36, 54, 72, 90, 108, 126, 144, 162, 180,198, 216, 234, 252, 270, 288, 306, 324, 342, 360.
b. 104 and 76 ________
Answer:
Least common multiple of 104 and 76: 1976.
Explanation:
Multiples of 104:
104, 208, 312, 416, 520, 624, 728, 832, 936, 1040, 1144, 1248, 1352, 1456, 1560, 1664, 1768, 1872, 1976, 2080.
Multiples of 76:
76, 152, 228, 304, 380, 456, 532, 608, 684, 760, 836, 912, 988, 1064, 1140, 1216, 1292, 1368, 1444, 1520, 1596, 1672, 1748, 1824, 1900, 1976, 2052, 2128, 2204, 2280.
Question 2.
a. 54 and 64 ________________
Answer:
Least common multiple of 54 and 64: 1728.
Explanation:
Multiples of 54:
54, 108, 162, 216, 270, 324, 378, 432, 486, 540, 594, 648, 702, 756, 810, 864, 918, 972, 1026, 1080, 1134, 1188, 1242, 1296, 1350, 1404, 1458, 1512, 1566, 1620, 1674, 1728.
Multiples of 64:
64, 128, 192, 256, 320, 384, 448, 512, 576, 640, 704, 768, 832, 896, 960, 1024, 1088, 1152, 1216, 1280, 1344, 1408, 1472, 1536, 1600, 1664, 1728, 1792, 1856, 1920, 1984
b. 20 and 26 ________
Answer:
Least common multiple of 20 and 26: 260.
Explanation:
Multiples of 20:
20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320, 340, 360, 380, 400, 420, 440, 460, 480, 500, 520, 540, 560.
Multiples of 26:
26, 52, 78, 104, 130, 156, 182, 208, 234, 260, 286, 312, 338, 364, 390, 416, 442, 468, 494, 520, 546, 572, 598, 624, 650, 676, 702, 728, 754, 780, 806, 832, 858, 884, 910.
Question 3.
a. 78 and 110 ____
Answer:
Least common multiple of 78 and 110: 4290.
Explanation:
Multiples of 78:
78, 78, 156, 234, 312, 390, 468, 546, 624, 702, 780, 858, 936, 1014, 1092, 1170, 1248, 1326, 1404, 1482, 1560, 1638, 1716, 1794, 1872, 1950, 2028, 2106, 2184, 2262, 2340, 2418, 2496, 2574, 2652, 2730, 2808, 2886, 2964, 3042, 3120, 3198, 3276, 3354, 3432, 3510, 3588, 3666, 3744, 3822, 3900, 3978, 4056, 4134, 4212, 4290.
Multiples of 110:
110, 220, 330, 440, 550, 660, 770, 880, 990, 1100, 1210, 1320, 1430, 1540, 1650, 1760, 1870, 1980, 2090, 2200, 2310, 2420, 2530, 2640, 2750, 2860, 2970, 3080, 3190, 3300, 3410, 3520, 3630, 3740, 3850, 3960, 4070, 4180, 4290, 4400, 4510, 4620, 4730, 4840, 4950, 5060, 5170, 5280, 5390.
b. 42 and 63 ____
Answer:
Least common multiple of 42 and 63: 126.
Explanation:
Multiples of 42:
42, 84, 126, 168, 210, 252, 294, 336, 378, 420.
Multiples of 63:
63, 126, 189, 252, 315, 378, 441, 504, 567, 630.
Question 4.
a. 23 and 92 ____
Answer:
Least common multiple of 23 and 92: 92.
Explanation:
Multiples of 23:
23, 46, 69, 92, 115, 138, 161, 184, 207, 230.
Multiples of 92:
92, 184, 276, 368, 460, 552, 644, 736, 828, 920.
b. 75 and 15 ____
Answer:
Least common multiple of 75 and 15: 75.
Explanation:
Multiples of 75:
75, 150, 225, 300, 375, 450, 525, 600, 675, 750.
Multiples of 15:
15, 30, 45, 60, 75, 90, 105, 120, 135, 150.
Question 5.
a. 28 and 32 ____
Answer:
Least common multiple of 28 and 32: 224.
Explanation:
Multiples of 28:
28, 56, 84, 112, 140, 168, 196, 224, 252, 280.
Multiples of 32:
32, 64, 96, 128, 160, 192, 224, 256, 288, 320, 352.
b. 12 and 16 ____
Answer:
Least common multiple of 12 and 16: 48.
Explanation:
Multiples of 12:
12, 24, 36, 48, 60, 72, 84, 96, 108, 120.
Multiples of 16:
16, 32, 48, 64, 80, 96, 112, 128, 144, 160.
Question 6.
a. 9, 45, and 81 ____
Answer:
Least common multiple of 9, 45, and 81: 405.
Explanation:
Multiples of 9:
9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 405.
Multiples of 45:
45, 90, 135, 180, 225, 270, 315, 360, 405, 450.
Multiples of 81:
81, 162, 243, 324, 405, 486, 567, 648, 729, 810.
b. 21, 45, and 6 ____
Answer:
Least common multiple of 21, 45, and 6: 630.
Explanation:
Multiples of 21:
21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420, 441, 462, 483, 504, 525, 546, 567, 588, 609, 630.
Multiples of 45:
90, 135, 180, 225, 270, 315, 360, 405, 450, 495, 540, 585, 630.
Multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 306, 312, 318, 324, 330, 336, 342, 348, 354, 360, 366, 372, 378, 384, 390, 396, 402, 408, 414, 420, 426, 432, 438, 444, 450, 456, 462, 468, 474, 480, 486, 492, 498, 504, 510, 516, 522, 528, 534, 540, 546, 552, 558, 564, 570, 576, 582, 588, 594, 600, 606, 612, 618, 624, 630.
Question 7.
a. 7, 4, and 13 ____
Answer:
Least common multiple of 7, 4, and 13: 364.
Explanation:
Multiples of 7:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 287, 294, 301, 308, 315, 322, 329, 336, 343, 350, 357, 364.
Multiples of 4:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196,200, 204, 208, 212, 216, 220, 224, 228, 232, 236, 240, 244, 248, 252, 256, 260, 264, 268, 272, 276, 282, 286, 290, 294, 298, 302, 306, 310, 314, 318, 322, 326, 340, 344, 348, 352, 356, 260, 364.
Multiples of 13:
13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299, 312, 325, 338, 351, 364,.
b. 6, 8 and 20 ________
Answer:
Least common multiple of 6, 8 and 20: 120.
Explanation:
Multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120.
Multiples of 8:
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120.
Multiples of 20:
20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240.
Find the least common multiple for each set of numbers.
Question 1.
a. 10 and 13 ____
Answer:
Least common multiple of 10 and 13: 130.
Explanation:
Multiples of 10:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200.
Multiples of 13:
13, 26, 39, 52, 65, 78, 91, 104, 117, 130.
b. 23 and 35 ____
Answer:
Least common multiple of 23 and 35: 805.
Explanation:
Multiples of 23:
23, 46, 69, 92, 115, 138, 161, 184, 207, 230, 253, 276, 299, 322, 345, 368, 391, 414, 437, 460, 483, 506, 529, 552, 575, 598, 621, 644, 667, 690, 713, 736, 759, 782, 805.
Multiples of 35:
35, , 70, 105, 140, 175, 210, 245, 280, 315, 350, 385, 420, 455, 490, 525, 560, 595, 630, 665, 700, 735, 770, 805.
Question 2.
a. 45 and 9 ____
Answer:
Least common multiple of 45 and 9: 45.
Explanation:
Multiples of 45:
45, 90, 135, 180, 225, 270, 315, 360, 405, 450.
Multiples of 9:
9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180.
b. 14 and 25 ____
Answer:
Least common multiple of 14 and 25: 350.
Explanation:
Multiples of 14:
14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280, 294, 308, 322, 336, 350.
Multiples of 25:
25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350.
Question 3.
a. 68 and 71 ____
Answer:
Least common multiple of 68 and 71: 4,828.
Explanation:
Multiples of 68:
68, 136, 204, 272, 340, 408, 476, 544, 612, 680, 748, 816, 884, 952, 1020, 1088, 1156, 1224, 1292, 1360, 1428, 1496, 1564, 1632, 1700, 1768, 1836, 1904, 1972, 2040, 2108, 2176, 2244, 2312, 2380, 2448, 2516, 2584, 2652, 2720, 2788, 2856, 2924, 2992, 3060, 3128, 3196, 3264, 3332, 3400, 3468, 3536, 3604, 3672, 3740, 3808, 3876, 3944, 4012, 4080, 4148, 4216, 4284,
4352, 4420, 4488, 4556, 4624, 4692, 4760, 4828.
Multiples of 71:
71, 142, 213, 284, 355, 426, 497, 568, 639, 710, 781, 852, 923, 994, 1065, 1136, 1207, 1278, 1349, 1420, 1491, 1562, 1633, 1704, 1775, 1846, 1917, 1988, 2059, 2130, 2201, 2272, 2343, 2414, 2485, 2556, 2627, 2698, 2769, 2840, 2911, 2982, 3053, 3124, 3195, 3266, 3337, 3408, 3479, 3550, 3621, 3692, 3763, 3834, 3905, 3976, 4047, 4118, 4189, 4260, 4331, 4402, 4473, 4544, 4615, 4686, 4757, 4828.
b. 63 and 76 ____
Answer:
Least common multiple of 63 and 76: 4788.
Explanation:
Multiples of 63:
63, 126, 189, 252, 315, 378, 441, 504, 567, 630, 693, 756, 819, 882, 945, 1008, 1071, 1134, 1197, 1260, 1323, 1386, 1449, 1512, 1575, 1638, 1701, 1764, 1827, 1890, 1953, 2016, 2079, 2142, 2205, 2268, 2331, 2394, 2457, 2520, 2583, 2646, 2709, 2772, 2835, 2898, 2961, 3024, 3087, 3150, 3213, 3276, 3339, 3402, 3465, 3528, 3591, 3654, 3717, 3780, 3843, 3906, 3969, 4032, 4095, 4158, 4221, 4284, 4347, 4410, 4473, 4636, 4599, 4662, 4725, 4788.
Multiples of 76:
76, 152, 228, 304, 380, 456, 532, 608, 684, 760, 836, 912, 988, 1064, 1140, 1216, 1292, 1368, 1444, 1520, 1596, 1672, 1748, 1824, 1900, 1976, 2052, 2128, 2204, 2280, 2356, 2432, 2508, 2584, 2660, 2736, 2812, 2888, 2964, 3040, 3116, 3192, 3268, 3344, 3420, 3496, 3572, 3648, 3724, 3800, 3876, 3952, 4028, 4104, 4180, 4256, 4332, 4408, 4484, 4560, 4636, 4712, 4788.
Question 4.
a. 28 and 35 ____
Answer:
Least common multiple of 28 and 35: 140.
Explanation:
Multiples of 28:
28, 56, 84, 112, 140, 168, 196, 224, 252, 280.
Multiples of 35:
35, 70, 105, 140, 175, 210, 245, 280, 315, 350.
b. 40 and 50 ____
Answer:
Least common multiple of 40 and 50: 200.
Explanation:
Multiples of 40:
40, 80, 120, 160, 200, 240, 280, 320, 360, 400.
Multiples of 50:
50, 100, 150, 200, 250, 300, 350, 400, 450, 500.
Question 5.
a. 33 and 44 ____
Answer:
Least common multiple of 33 and 44: 132.
Explanation:
Multiples of 33:
66, 99, 132, 165, 198, 231, 264, 297, 330.
Multiples of 44:
44, 88, 132, 176, 220, 264, 308, 352, 396, 440.
b. 27 and 45 ____
Answer:
Least common multiple of 27 and 45: 135.
Explanation:
Multiples of 27:
27, 54, 81, 108, 135, 162, 189, 216, 243, 270.
Multiples of 45:
45, 90, 135, 180, 225, 270, 315, 360, 405, 450.
Question 6.
a. 6, 26, and 18 ____
Answer:
Least common multiple of 6, 26, and 18: 234.
Explanation:
Multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240.
Multiples of 26:
26, 52, 78, 104, 130, 156, 182, 208, 234, 260.
Multiples of 18:
18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, 270.
b. 4, 24, and 21 ____
Answer:
Least common multiple of 4, 24, and 21: 168.
Explanation:
Multiples of 4:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180.
Multiples of 24:
24, 48, 72, 96, 120, 144, 168, 192, 216, 240.
Multiples of 21:
21, 42, 63, 84, 105, 126, 147, 168, 189, 210.
Question 7.
a. 5, 25, and 65 ____
Answer:
Least common multiple of 5, 25, and 65: 325.
Explanation:
Multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245,250, 255, 260, 265, 270, 275, 280, 285, 290, 295, 300, 305, 310, 315, 320, 325, 330.
Multiples of 25:
25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350.
Multiples of 65:
65, 130, 195, 260, 325, 390, 455, 520, 585, 650.
b. 7, 19, and 14 ____
Answer:
Least common multiple of 7, 19, and 14: 266.
Explanation:
Multiples of 7:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280.
Multiples of 19:
19, 38, 57, 76, 95, 114, 133, 152, 171, 190, 209, 228, 247, 266, 285.
Multiples of 14:
14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280.
Question 8.
a. 3, 27, and 45 ____
Answer:
Least common multiple of 3, 27, and 45: 135.
Explanation:
Multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138.
Multiples of 27:
27, 54, 81, 108, 135, 162, 189, 216, 243, 270.
Multiples of 45:
45, 90, 135, 180, 225, 270, 315, 360, 405, 450.
b. 8, 72, and 216 ____
Answer:
Least common multiple of 8, 72, and 216: 216.
Explanation:
Multiples of 8:
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280.
Multiples of 72:
72, 144, 216, 288, 360, 432, 504, 576, 648, 720.
Multiples of 216:
216, 432, 648, 864, 1080, 1296, 1512, 1728, 1944, 2160.