LCM of 96 and 404: How to find LCM of 96 and 404?

The LCM of 96 and 404 is 9696. Least Common Multiple (LCM) of two numbers is the smallest number that both are factors of. In this blog, we’ll explain easy ways to find the LCM of 96 and 404.

How to Find the LCM of 96 and 404

Here are three simple ways to find the LCM of 96 and 404:

1. Prime Factorization Method

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

• 96 = 2 × 2 × 2 × 2 × 2 × 3 (or 2⁵ × 3)
• 404 = 2 × 2 × 101 (or 2² × 101)
• Using the highest powers: 2⁵ × 3 × 101 = 9,696

Thus, LCM(96, 404) = 9,696.

2. Listing Multiples Method

List the multiples of both numbers and find the smallest common one.

• Multiples of 96: 96, 192, 288, 384, ..., 9,696, ...
• Multiples of 404: 404, 808, 1,212, ..., 9,696, ...
• The smallest common multiple is 9,696.

Thus, LCM(96, 404) = 9,696.

3. Division Method

Divide both numbers by common factors until you get 1.

1. Divide 96 and 404 by 2 → (48, 202)
2. Divide 48 and 202 by 2 → (24, 101)
3. Both 24 and 101 is divisible by 1.
4. Multiply the divisors: 2 × 2 × 24 × 101 = 9,696

Thus, LCM(96, 404) = 9,696.

Conclusion

The LCM of 96 and 404 is 9,696, and you can find it using prime factorization, listing multiples, or division.