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.

How 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 only 1 remains.

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 2 → (2, 3, 9)
5. Divide 2, 3, and 9 by 3 → (2, 1, 3)
6. 2, 1, 3 are divisible by 1 only
7. Multiply the divisors: 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432

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

Conclusion

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