What is the Least Common Multiple of 45138 and 45144?

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 45138 and 45144 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45138 and 45144, than apply into the LCM equation.

GCF(45138,45144) = 6
LCM(45138,45144) = ( 45138 × 45144) / 6
LCM(45138,45144) = 2037709872 / 6
LCM(45138,45144) = 339618312

Least Common Multiple (LCM) of 45138 and 45144 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45138 and 45144. First we will calculate the prime factors of 45138 and 45144.

Prime Factorization of 45138

Prime Factorization of 45144

Now multiplying the highest exponent prime factors to calculate the LCM of 45138 and 45144.

LCM(45138,45144) = 2³ × 3³ × 7523¹ × 11¹ × 19¹
LCM(45138,45144) = 339618312