What is the Least Common Multiple of 32670 and 32688?

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 32670 and 32688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32670 and 32688, than apply into the LCM equation.

GCF(32670,32688) = 18
LCM(32670,32688) = ( 32670 × 32688) / 18
LCM(32670,32688) = 1067916960 / 18
LCM(32670,32688) = 59328720

Least Common Multiple (LCM) of 32670 and 32688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32670 and 32688. First we will calculate the prime factors of 32670 and 32688.

Prime Factorization of 32670

Prime Factorization of 32688

Now multiplying the highest exponent prime factors to calculate the LCM of 32670 and 32688.

LCM(32670,32688) = 2⁴ × 3³ × 5¹ × 11² × 227¹
LCM(32670,32688) = 59328720