What is the Least Common Multiple of 37638 and 37656?

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 37638 and 37656 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37638 and 37656, than apply into the LCM equation.

GCF(37638,37656) = 18
LCM(37638,37656) = ( 37638 × 37656) / 18
LCM(37638,37656) = 1417296528 / 18
LCM(37638,37656) = 78738696

Least Common Multiple (LCM) of 37638 and 37656 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37638 and 37656. First we will calculate the prime factors of 37638 and 37656.

Prime Factorization of 37638

Prime Factorization of 37656

Now multiplying the highest exponent prime factors to calculate the LCM of 37638 and 37656.

LCM(37638,37656) = 2³ × 3³ × 17¹ × 41¹ × 523¹
LCM(37638,37656) = 78738696