What is the Least Common Multiple of 75672 and 75684?

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 of 75672 and 75684 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75672 and 75684, than apply into the LCM equation.

GCF(75672,75684) = 12
LCM(75672,75684) = ( 75672 × 75684) / 12
LCM(75672,75684) = 5727159648 / 12
LCM(75672,75684) = 477263304

Least Common Multiple (LCM) of 75672 and 75684 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75672 and 75684. First we will calculate the prime factors of 75672 and 75684.

Prime Factorization of 75672

Prime Factorization of 75684

Now multiplying the highest exponent prime factors to calculate the LCM of 75672 and 75684.

LCM(75672,75684) = 2³ × 3² × 1051¹ × 7¹ × 17¹ × 53¹
LCM(75672,75684) = 477263304