What is the Least Common Multiple of 37584 and 37596?

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 37584 and 37596 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37584 and 37596, than apply into the LCM equation.

GCF(37584,37596) = 12
LCM(37584,37596) = ( 37584 × 37596) / 12
LCM(37584,37596) = 1413008064 / 12
LCM(37584,37596) = 117750672

Least Common Multiple (LCM) of 37584 and 37596 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37584 and 37596. First we will calculate the prime factors of 37584 and 37596.

Prime Factorization of 37584

Prime Factorization of 37596

Now multiplying the highest exponent prime factors to calculate the LCM of 37584 and 37596.

LCM(37584,37596) = 2⁴ × 3⁴ × 29¹ × 13¹ × 241¹
LCM(37584,37596) = 117750672