What is the Least Common Multiple of 30564 and 30576?

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 30564 and 30576 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30564 and 30576, than apply into the LCM equation.

GCF(30564,30576) = 12
LCM(30564,30576) = ( 30564 × 30576) / 12
LCM(30564,30576) = 934524864 / 12
LCM(30564,30576) = 77877072

Least Common Multiple (LCM) of 30564 and 30576 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30564 and 30576. First we will calculate the prime factors of 30564 and 30576.

Prime Factorization of 30564

Prime Factorization of 30576

Now multiplying the highest exponent prime factors to calculate the LCM of 30564 and 30576.

LCM(30564,30576) = 2⁴ × 3³ × 283¹ × 7² × 13¹
LCM(30564,30576) = 77877072