What is the Least Common Multiple of 42123 and 42135?

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 42135 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 42135, than apply into the LCM equation.

GCF(42123,42135) = 3
LCM(42123,42135) = ( 42123 × 42135) / 3
LCM(42123,42135) = 1774852605 / 3
LCM(42123,42135) = 591617535

Least Common Multiple (LCM) of 42123 and 42135 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42123 and 42135. First we will calculate the prime factors of 42123 and 42135.

Prime Factorization of 42123

Prime Factorization of 42135

Now multiplying the highest exponent prime factors to calculate the LCM of 42123 and 42135.

LCM(42123,42135) = 3¹ × 19¹ × 739¹ × 5¹ × 53²
LCM(42123,42135) = 591617535