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What is the Least Common Multiple of 54672 and 54688?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 54672 and 54688 is 186868896.

LCM(54672,54688) = 186868896

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Least Common Multiple of 54672 and 54688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54672 and 54688, than apply into the LCM equation.

GCF(54672,54688) = 16
LCM(54672,54688) = ( 54672 × 54688) / 16
LCM(54672,54688) = 2989902336 / 16
LCM(54672,54688) = 186868896

Least Common Multiple (LCM) of 54672 and 54688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54672 and 54688. First we will calculate the prime factors of 54672 and 54688.

Prime Factorization of 54672

Prime factors of 54672 are 2, 3, 17, 67. Prime factorization of 54672 in exponential form is:

54672 = 24 × 31 × 171 × 671

Prime Factorization of 54688

Prime factors of 54688 are 2, 1709. Prime factorization of 54688 in exponential form is:

54688 = 25 × 17091

Now multiplying the highest exponent prime factors to calculate the LCM of 54672 and 54688.

LCM(54672,54688) = 25 × 31 × 171 × 671 × 17091
LCM(54672,54688) = 186868896