What is the Least Common Multiple of 51180 and 51200?

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 51180 and 51200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51180 and 51200, than apply into the LCM equation.

GCF(51180,51200) = 20
LCM(51180,51200) = ( 51180 × 51200) / 20
LCM(51180,51200) = 2620416000 / 20
LCM(51180,51200) = 131020800

Least Common Multiple (LCM) of 51180 and 51200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51180 and 51200. First we will calculate the prime factors of 51180 and 51200.

Prime Factorization of 51180

Prime Factorization of 51200

Now multiplying the highest exponent prime factors to calculate the LCM of 51180 and 51200.

LCM(51180,51200) = 2¹¹ × 3¹ × 5² × 853¹
LCM(51180,51200) = 131020800