What is the Least Common Multiple of 30144 and 30153?

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 30144 and 30153 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30144 and 30153, than apply into the LCM equation.

GCF(30144,30153) = 3
LCM(30144,30153) = ( 30144 × 30153) / 3
LCM(30144,30153) = 908932032 / 3
LCM(30144,30153) = 302977344

Least Common Multiple (LCM) of 30144 and 30153 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30144 and 30153. First we will calculate the prime factors of 30144 and 30153.

Prime Factorization of 30144

Prime Factorization of 30153

Now multiplying the highest exponent prime factors to calculate the LCM of 30144 and 30153.

LCM(30144,30153) = 2⁶ × 3¹ × 157¹ × 19¹ × 23²
LCM(30144,30153) = 302977344