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LCM of 48, 72 and 108: How to find LCM of 48, 72 and 108?

The LCM of 48, 72, and 108 is 432. Least Common Multiple (LCM) of a group of numbers is the smallest number that all of them can fit into. In this blog, we’ll explain easy ways to find the LCM of 48, 72, and 108.

Methods to find the LCM of 48, 72, and 108

Here are three simple methods to find the LCM of 48, 72, and 108:

1. Prime Factorization Method

Break each number into its prime factors and use the highest power of each factor.

  • 48 = 2 × 2 × 2 × 2 × 3 (or 2⁴ × 3)
  • 72 = 2 × 2 × 2 × 3 × 3 (or 2³ × 3²)
  • 108 = 2 × 2 × 3 × 3 × 3 (or 2² × 3³)
  • Taking the highest powers: 2⁴ × 3³ = 432

Thus, LCM(48, 72, 108) = 432.


2. Listing Multiples Method

List the multiples of each number and find the smallest one they all share.

Multiples of 48: 48, 96, 144, 192, 240, 288, 336, 384, 432, ...
Multiples of 72: 72, 144, 216, 288, 360, 432, ...
Multiples of 108: 108, 216, 324, 432, ...

The smallest common multiple is 432.

Thus, LCM(48, 72, 108) = 432.


3. Division Method

Divide all numbers by common factors until at least 2 numbers are divisible.

1. Divide 48, 72, and 108 by 2 → (24, 36, 54)
2. Divide 24, 36, and 54 by 2 → (12, 18, 27)
3. Divide 12, 18, and 27 by 3 → (4, 6, 9)
4. Divide 4, 6, and 9 by 3 → (4, 2, 3)
5. Divide 4, 2, and 3 by 2 → (2, 1, 3)
6. 2, 1, and 3 are divisible by 1 only.

Multiply the divisors:
2 × 2 × 3 × 3 × 2 × 2 × 3 = 432

Thus, LCM(48, 72, 108) = 432.

Know how to find the LCM of 4 and 6 here.

Conclusion:

The LCM of 48, 72, and 108 is 432, and you can find it using prime factorization, listing multiples, or division.


FAQs

1. How to find LCM?

To find the LCM:

  1. Break the numbers into prime factors.

  2. Take the highest powers of all prime factors.

  3. Multiply them together.

Example: LCM of 12 and 18

  • 12 = 2² × 3, 18 = 2 × 3²

  • LCM = 2² × 3² = 36.

2. How do you find the LCM of 48 and 108?

To find the LCM of 48 and 108:

  1. Prime factorization of 48 = 2⁴ × 3.

  2. Prime factorization of 108 = 2² × 3³.

  3. Take the highest power of each prime factor:
    LCM = 2⁴ × 3³ = 16 × 27 = 432.

So, the LCM of 48 and 108 is 432.

3. How do you find the LCM of 72 and 108?

To find the LCM of 72 and 108:

  1. Prime factorization of 72 = 2³ × 3².

  2. Prime factorization of 108 = 2² × 3³.

  3. Take the highest power of each prime factor:
    LCM = 2³ × 3³ = 72 × 27 = 1944.

So, the LCM of 72 and 108 is 1944.

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