What is the Least Common Multiple of 30135 and 30144?

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 30135 and 30144 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30135 and 30144, than apply into the LCM equation.

GCF(30135,30144) = 3
LCM(30135,30144) = ( 30135 × 30144) / 3
LCM(30135,30144) = 908389440 / 3
LCM(30135,30144) = 302796480

Least Common Multiple (LCM) of 30135 and 30144 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30135 and 30144. First we will calculate the prime factors of 30135 and 30144.

Prime Factorization of 30135

Prime Factorization of 30144

Now multiplying the highest exponent prime factors to calculate the LCM of 30135 and 30144.

LCM(30135,30144) = 3¹ × 5¹ × 7² × 41¹ × 2⁶ × 157¹
LCM(30135,30144) = 302796480