What is the Least Common Multiple of 30120 and 30132?

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 30132 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 30132, than apply into the LCM equation.

GCF(30120,30132) = 12
LCM(30120,30132) = ( 30120 × 30132) / 12
LCM(30120,30132) = 907575840 / 12
LCM(30120,30132) = 75631320

Least Common Multiple (LCM) of 30120 and 30132 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30120 and 30132. First we will calculate the prime factors of 30120 and 30132.

Prime Factorization of 30120

Prime Factorization of 30132

Now multiplying the highest exponent prime factors to calculate the LCM of 30120 and 30132.

LCM(30120,30132) = 2³ × 3⁵ × 5¹ × 251¹ × 31¹
LCM(30120,30132) = 75631320