What is the Least Common Multiple of 45144 and 45156?

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 45144 and 45156 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45144 and 45156, than apply into the LCM equation.

GCF(45144,45156) = 12
LCM(45144,45156) = ( 45144 × 45156) / 12
LCM(45144,45156) = 2038522464 / 12
LCM(45144,45156) = 169876872

Least Common Multiple (LCM) of 45144 and 45156 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45144 and 45156. First we will calculate the prime factors of 45144 and 45156.

Prime Factorization of 45144

Prime Factorization of 45156

Now multiplying the highest exponent prime factors to calculate the LCM of 45144 and 45156.

LCM(45144,45156) = 2³ × 3³ × 11¹ × 19¹ × 53¹ × 71¹
LCM(45144,45156) = 169876872