What is the Least Common Multiple of 30128 and 30146?

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 30128 and 30146 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30128 and 30146, than apply into the LCM equation.

GCF(30128,30146) = 2
LCM(30128,30146) = ( 30128 × 30146) / 2
LCM(30128,30146) = 908238688 / 2
LCM(30128,30146) = 454119344

Least Common Multiple (LCM) of 30128 and 30146 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30128 and 30146. First we will calculate the prime factors of 30128 and 30146.

Prime Factorization of 30128

Prime Factorization of 30146

Now multiplying the highest exponent prime factors to calculate the LCM of 30128 and 30146.

LCM(30128,30146) = 2⁴ × 7¹ × 269¹ × 15073¹
LCM(30128,30146) = 454119344