What is the Least Common Multiple of 30420 and 30432?

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 30420 and 30432 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30420 and 30432, than apply into the LCM equation.

GCF(30420,30432) = 12
LCM(30420,30432) = ( 30420 × 30432) / 12
LCM(30420,30432) = 925741440 / 12
LCM(30420,30432) = 77145120

Least Common Multiple (LCM) of 30420 and 30432 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30420 and 30432. First we will calculate the prime factors of 30420 and 30432.

Prime Factorization of 30420

Prime Factorization of 30432

Now multiplying the highest exponent prime factors to calculate the LCM of 30420 and 30432.

LCM(30420,30432) = 2⁵ × 3² × 5¹ × 13² × 317¹
LCM(30420,30432) = 77145120