What is the Least Common Multiple of 90123 and 90135?

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 90123 and 90135 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90123 and 90135, than apply into the LCM equation.

GCF(90123,90135) = 3
LCM(90123,90135) = ( 90123 × 90135) / 3
LCM(90123,90135) = 8123236605 / 3
LCM(90123,90135) = 2707745535

Least Common Multiple (LCM) of 90123 and 90135 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90123 and 90135. First we will calculate the prime factors of 90123 and 90135.

Prime Factorization of 90123

Prime Factorization of 90135

Now multiplying the highest exponent prime factors to calculate the LCM of 90123 and 90135.

LCM(90123,90135) = 3² × 11¹ × 2731¹ × 5¹ × 2003¹
LCM(90123,90135) = 2707745535