What is the Least Common Multiple of 15180 and 15200?

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 15180 and 15200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15180 and 15200, than apply into the LCM equation.

GCF(15180,15200) = 20
LCM(15180,15200) = ( 15180 × 15200) / 20
LCM(15180,15200) = 230736000 / 20
LCM(15180,15200) = 11536800

Least Common Multiple (LCM) of 15180 and 15200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 15180 and 15200. First we will calculate the prime factors of 15180 and 15200.

Prime Factorization of 15180

Prime Factorization of 15200

Now multiplying the highest exponent prime factors to calculate the LCM of 15180 and 15200.

LCM(15180,15200) = 2⁵ × 3¹ × 5² × 11¹ × 23¹ × 19¹
LCM(15180,15200) = 11536800