What is the Least Common Multiple of 30624 and 30639?

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 30624 and 30639 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30624 and 30639, than apply into the LCM equation.

GCF(30624,30639) = 3
LCM(30624,30639) = ( 30624 × 30639) / 3
LCM(30624,30639) = 938288736 / 3
LCM(30624,30639) = 312762912

Least Common Multiple (LCM) of 30624 and 30639 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30624 and 30639. First we will calculate the prime factors of 30624 and 30639.

Prime Factorization of 30624

Prime Factorization of 30639

Now multiplying the highest exponent prime factors to calculate the LCM of 30624 and 30639.

LCM(30624,30639) = 2⁵ × 3¹ × 11¹ × 29¹ × 7¹ × 1459¹
LCM(30624,30639) = 312762912