What is the Least Common Multiple of 30612 and 30624?

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 30612 and 30624 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30612 and 30624, than apply into the LCM equation.

GCF(30612,30624) = 12
LCM(30612,30624) = ( 30612 × 30624) / 12
LCM(30612,30624) = 937461888 / 12
LCM(30612,30624) = 78121824

Least Common Multiple (LCM) of 30612 and 30624 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30612 and 30624. First we will calculate the prime factors of 30612 and 30624.

Prime Factorization of 30612

Prime Factorization of 30624

Now multiplying the highest exponent prime factors to calculate the LCM of 30612 and 30624.

LCM(30612,30624) = 2⁵ × 3¹ × 2551¹ × 11¹ × 29¹
LCM(30612,30624) = 78121824