What is the Least Common Multiple of 32100 and 32120?

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 32100 and 32120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32100 and 32120, than apply into the LCM equation.

GCF(32100,32120) = 20
LCM(32100,32120) = ( 32100 × 32120) / 20
LCM(32100,32120) = 1031052000 / 20
LCM(32100,32120) = 51552600

Least Common Multiple (LCM) of 32100 and 32120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32100 and 32120. First we will calculate the prime factors of 32100 and 32120.

Prime Factorization of 32100

Prime Factorization of 32120

Now multiplying the highest exponent prime factors to calculate the LCM of 32100 and 32120.

LCM(32100,32120) = 2³ × 3¹ × 5² × 107¹ × 11¹ × 73¹
LCM(32100,32120) = 51552600