The abbreviation of L.C.M is Least Common Multiple. In order to find the L.C.M of two or more numbers, we have to find the prime factors of the given numbers. The Least Common Multiple or Smaller Common Multiple is the lowest possible number that can be divisible by both numbers.

Prime factorization is one of the methods to find the L.C.M of two or more numbers. Examples to find Least Common Multiple by using Prime Factorization Method are discussed on this page. So, the students who wish to become masters in maths are suggested to follow 5th Grade Math and practice the questions.

**Do Refer:**

- To find Least Common Multiple by using Prime Factorization Method
- Method of L.C.M
- Properties of L.C.M
- Worksheet on Methods of H.C.F and L.C.M

## Examples to find L.C.M by using Prime Factorization Method

**Question 1.**

What is the least common multiple of 28 and 63 by using the prime factorization method?

**Solution:**

List all prime factors for each number.

Prime factorization of 28 is 2 × 2 × 7

Prime factorization of 63 is 3 × 3 × 7

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

Multiply these factors together to find the LCM.

L.C.M = 2 × 2 × 3 × 3 × 7 = 252

Thus the LCM of 28 and 63 is 252.

lcm(28, 63) = 252

**Question 2.**

What is the least common multiple of 12 and 36 by using the prime factorization method?

**Solution:**

List all prime factors for each number.

Prime factorization of 12 is 2 × 2 × 3

Prime factorization of 36 is 2 × 2 × 3 × 3

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

2, 2, 3, 3

Multiply these factors together to find the LCM.

L.C.M = 2 × 2 × 3 × 3 = 36

Thus the LCM of 12 and 36 is 36.

lcm(12, 36) = 36.

**Question 3.**

What is the least common multiple of 72 and 108 by using the prime factorization method?

**Solution:**

List all prime factors for each number.

Prime factorization of 72 is 2 × 2 × 2 × 3 × 3

Prime factorization of 108 is 2 × 2 × 3 × 3 × 3

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

2, 2, 2, 3, 3, 3

Multiply these factors together to find the LCM.

L.C.M = 2 × 2 × 2 × 3 × 3 × 3 = 216

Thus the LCM of 72 and 108 is 216.

lcm(72, 108) = 216.

**Question 4.**

What is the least common multiple of 15 and 75 by using the prime factorization method?

**Solution:**

List all prime factors for each number.

Prime factorization of 15 is 3 × 5

Prime factorization of 75 is 3 × 5 × 5

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

3, 5, 5

Multiply these factors together to find the LCM.

L.C.M = 3 × 5 × 5 = 75

Thus the LCM of 15 and 75 is 75.

lcm(15, 75) = 75.

**Question 5.**

What is the least common multiple of 13 and 91 by using the prime factorization method?

**Solution:**

List all prime factors for each number.

Prime factorization of 13 is 13

Prime factorization of 91 is 13 × 7

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

7, 13

Multiply these factors together to find the LCM.

L.C.M = 7 × 13 = 91

Thus the LCM of 13 and 91 is 91.

lcm(13, 91) = 91.

**Question 6.**

What is the least common multiple of 4, 6, and 36 by using the prime factorization method?

**Solution:**

List all prime factors for each number.

Prime factorization of 4 is 2 × 2

Prime factorization of 6 is 2 × 3

Prime factorization of 36 is 2 × 2 × 3 × 3

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

2, 2, 3, 3

Multiply these factors together to find the LCM.

L.C.M = 2 × 2 × 3 × 3 = 36

Thus the LCM of 4, 6 and 36 is 36.

lcm(4, 6, 36) = 36.

**Question 7.**

What is the least common multiple of 3, 18 and 72 by using the prime factorization method?

**Solution:**

List all prime factors for each number.

Prime factorization of 3 is 3

Prime factorization of 18 is 2 × 3 × 3

Prime factorization of 72 is 2 × 2 × 2 × 3 × 3

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

2, 2, 2, 3, 3

Multiply these factors together to find the LCM.

L.C.M = 2 × 2 × 2 × 3 × 3 = 72

Thus the LCM of 3, 18 and 72 is 72.

lcm(3, 18, 72) = 72.

**Question 8.**

What is the least common multiple of 25 and 90 by using the prime factorization method?

**Solution:**

List all prime factors for each number.

Prime factorization of 25 is 5 × 5

Prime factorization of 90 is 2 × 3 × 3 × 5

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

2, 3, 3, 5, 5

Multiply these factors together to find the LCM.

L.C.M = 2 × 3 × 3 × 5 × 5 = 450

Thus the LCM of 25 and 90 is 450.

lcm(25, 90) = 450.

**Question 9.**

What is the least common multiple of 6, 12 and 18 by using the prime factorization method?

**Solution:**

List all prime factors for each number.

Prime factorization of 6 is 2 × 3

Prime factorization of 12 is 2 × 2 × 3

Prime factorization of 18 is 2 × 3 × 3

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

2, 2, 3, 3

Multiply these factors together to find the LCM.

L.C.M = 2 × 2 × 3 × 3 = 36

Thus the LCM of 6, 12 and 18 is 36.

lcm(6, 12, 18) = 36.

**Question 10.**

What is the least common multiple of 8 and 56 by using the prime factorization method?

**Solution:**

List all prime factors for each number.

Prime factorization of 8 is 2 × 2 × 2

Prime factorization of 56 is 2 × 2 × 2 × 7

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

2, 2, 2, 7

Multiply these factors together to find the LCM.

L.C.M = 2 × 2 × 2 × 7 = 56

Thus the LCM of 8 and 56 is 56.

lcm(8, 56) = 56.