What is the Least Common Multiple of 42138 and 42144?

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 42138 and 42144 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42138 and 42144, than apply into the LCM equation.

GCF(42138,42144) = 6
LCM(42138,42144) = ( 42138 × 42144) / 6
LCM(42138,42144) = 1775863872 / 6
LCM(42138,42144) = 295977312

Least Common Multiple (LCM) of 42138 and 42144 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42138 and 42144. First we will calculate the prime factors of 42138 and 42144.

Prime Factorization of 42138

Prime Factorization of 42144

Now multiplying the highest exponent prime factors to calculate the LCM of 42138 and 42144.

LCM(42138,42144) = 2⁵ × 3² × 2341¹ × 439¹
LCM(42138,42144) = 295977312