What is the Least Common Multiple of 32700 and 32712?

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 32700 and 32712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32700 and 32712, than apply into the LCM equation.

GCF(32700,32712) = 12
LCM(32700,32712) = ( 32700 × 32712) / 12
LCM(32700,32712) = 1069682400 / 12
LCM(32700,32712) = 89140200

Least Common Multiple (LCM) of 32700 and 32712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32700 and 32712. First we will calculate the prime factors of 32700 and 32712.

Prime Factorization of 32700

Prime Factorization of 32712

Now multiplying the highest exponent prime factors to calculate the LCM of 32700 and 32712.

LCM(32700,32712) = 2³ × 3¹ × 5² × 109¹ × 29¹ × 47¹
LCM(32700,32712) = 89140200