What is the Least Common Multiple of 58800 and 58812?

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 58800 and 58812 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 58800 and 58812, than apply into the LCM equation.

GCF(58800,58812) = 12
LCM(58800,58812) = ( 58800 × 58812) / 12
LCM(58800,58812) = 3458145600 / 12
LCM(58800,58812) = 288178800

Least Common Multiple (LCM) of 58800 and 58812 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 58800 and 58812. First we will calculate the prime factors of 58800 and 58812.

Prime Factorization of 58800

Prime Factorization of 58812

Now multiplying the highest exponent prime factors to calculate the LCM of 58800 and 58812.

LCM(58800,58812) = 2⁴ × 3¹ × 5² × 7² × 13² × 29¹
LCM(58800,58812) = 288178800