LCM of 48, 72 and 92: How to find LCM of 48, 72 and 92?

The LCM of 48, 72 and 92 is 3312. 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 92.

Methods to find the LCM of 48, 72, and 92

Here are three simple methods to find the LCM of 48, 72, and 92:

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)
• 92 = 2 × 2 × 23 (or 2² × 23)
• Taking the highest powers: 2⁴ × 3² × 23 = 3312

Thus, LCM(48, 72, 92) = 3312.

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, ..., 3216, 3264, 3312, ...
• Multiples of 72: 72, 144, 216, 288, 360, ..., 3168, 3240, 3312, ...
• Multiples of 92: 92, 184, 276, 368, 460, ..., 3128, 3220, 3312, ...
• The smallest common multiple is 3312.

Thus, LCM(48, 72, 92) = 3312.

3. Division Method

Divide all numbers by common factors until only 1 remains.

1. Divide 48, 72, and 92 by 2 → (24, 36, 46)
2. Divide 24, 36, and 46 by 2 → (12, 18, 23)
3. Divide 12, 18 by 3 → (4, 6, 23)
4. Divide 4, 6, and 9 by 2 → (2, 3, 23)
5. 2, 3 and 23 are divisible by 1 only
6. Multiply the divisors: 2 × 2 × 2 × 2 × 3 × 3 × 23 = 3312

Thus, LCM(48, 72, 92) = 3312.

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

Conclusion:

The LCM of 48, 72, and 92 is 3312, and you can find it using prime factorization, listing multiples, or division.