What is the Least Common Multiple of 42123 and 42132?

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 42123 and 42132 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42123 and 42132, than apply into the LCM equation.

GCF(42123,42132) = 3
LCM(42123,42132) = ( 42123 × 42132) / 3
LCM(42123,42132) = 1774726236 / 3
LCM(42123,42132) = 591575412

Least Common Multiple (LCM) of 42123 and 42132 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42123 and 42132. First we will calculate the prime factors of 42123 and 42132.

Prime Factorization of 42123

Prime Factorization of 42132

Now multiplying the highest exponent prime factors to calculate the LCM of 42123 and 42132.

LCM(42123,42132) = 3¹ × 19¹ × 739¹ × 2² × 3511¹
LCM(42123,42132) = 591575412