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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.

Methods 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 at least 2 numbers are divisible.

  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.

Know how to find the lcm of 336 and 54 here.

Conclusion:

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

FAQs

1. What is the LCM of 96 and 404?

The Least Common Multiple (LCM) of 96 and 404 is 9696. This is the smallest positive integer that is divisible by both 96 and 404 without leaving any remainder. 

2. How to Find the LCM of 96 and 404 Using Prime Factorization?

To find the LCM using prime factorization:

  • Prime factorization of 96: 2⁵ × 3

  • Prime factorization of 404: 2² × 101​

The LCM is obtained by multiplying the highest powers of all prime factors present in either number:​

LCM = 2⁵ × 3 × 101 = 9696 ​

3. How to Find the LCM of 96 and 404 Using the Division Method?

The division method involves dividing the numbers by their common prime factors:​

  1. Divide both numbers by 2: 96 ÷ 2 = 48; 404 ÷ 2 = 202

  2. Divide the resulting numbers by 2: 48 ÷ 2 = 24; 202 ÷ 2 = 101

  3. Continue dividing by prime numbers until all resulting numbers are 1.

  4. Multiply all the prime divisors used: 2 × 2 × 2 × 2 × 2 × 3 × 101 = 9696

 

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