What is the Least Common Multiple of 37572 and 37584?

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 37572 and 37584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37572 and 37584, than apply into the LCM equation.

GCF(37572,37584) = 12
LCM(37572,37584) = ( 37572 × 37584) / 12
LCM(37572,37584) = 1412106048 / 12
LCM(37572,37584) = 117675504

Least Common Multiple (LCM) of 37572 and 37584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37572 and 37584. First we will calculate the prime factors of 37572 and 37584.

Prime Factorization of 37572

Prime Factorization of 37584

Now multiplying the highest exponent prime factors to calculate the LCM of 37572 and 37584.

LCM(37572,37584) = 2⁴ × 3⁴ × 31¹ × 101¹ × 29¹
LCM(37572,37584) = 117675504