What is the Least Common Multiple of 42504 and 42512?

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 42504 and 42512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42504 and 42512, than apply into the LCM equation.

GCF(42504,42512) = 8
LCM(42504,42512) = ( 42504 × 42512) / 8
LCM(42504,42512) = 1806930048 / 8
LCM(42504,42512) = 225866256

Least Common Multiple (LCM) of 42504 and 42512 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42504 and 42512. First we will calculate the prime factors of 42504 and 42512.

Prime Factorization of 42504

Prime Factorization of 42512

Now multiplying the highest exponent prime factors to calculate the LCM of 42504 and 42512.

LCM(42504,42512) = 2⁴ × 3¹ × 7¹ × 11¹ × 23¹ × 2657¹
LCM(42504,42512) = 225866256