What is the Least Common Multiple of 45180 and 45200?

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 45180 and 45200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45180 and 45200, than apply into the LCM equation.

GCF(45180,45200) = 20
LCM(45180,45200) = ( 45180 × 45200) / 20
LCM(45180,45200) = 2042136000 / 20
LCM(45180,45200) = 102106800

Least Common Multiple (LCM) of 45180 and 45200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45180 and 45200. First we will calculate the prime factors of 45180 and 45200.

Prime Factorization of 45180

Prime Factorization of 45200

Now multiplying the highest exponent prime factors to calculate the LCM of 45180 and 45200.

LCM(45180,45200) = 2⁴ × 3² × 5² × 251¹ × 113¹
LCM(45180,45200) = 102106800