What is the Least Common Multiple of 90120 and 90138?

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 90120 and 90138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90120 and 90138, than apply into the LCM equation.

GCF(90120,90138) = 6
LCM(90120,90138) = ( 90120 × 90138) / 6
LCM(90120,90138) = 8123236560 / 6
LCM(90120,90138) = 1353872760

Least Common Multiple (LCM) of 90120 and 90138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90120 and 90138. First we will calculate the prime factors of 90120 and 90138.

Prime Factorization of 90120

Prime Factorization of 90138

Now multiplying the highest exponent prime factors to calculate the LCM of 90120 and 90138.

LCM(90120,90138) = 2³ × 3¹ × 5¹ × 751¹ × 83¹ × 181¹
LCM(90120,90138) = 1353872760