What is the Least Common Multiple of 30120 and 30128?

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 30120 and 30128 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30120 and 30128, than apply into the LCM equation.

GCF(30120,30128) = 8
LCM(30120,30128) = ( 30120 × 30128) / 8
LCM(30120,30128) = 907455360 / 8
LCM(30120,30128) = 113431920

Least Common Multiple (LCM) of 30120 and 30128 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30120 and 30128. First we will calculate the prime factors of 30120 and 30128.

Prime Factorization of 30120

Prime Factorization of 30128

Now multiplying the highest exponent prime factors to calculate the LCM of 30120 and 30128.

LCM(30120,30128) = 2⁴ × 3¹ × 5¹ × 251¹ × 7¹ × 269¹
LCM(30120,30128) = 113431920