What is the Least Common Multiple of 30960 and 30972?

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 30960 and 30972 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30960 and 30972, than apply into the LCM equation.

GCF(30960,30972) = 12
LCM(30960,30972) = ( 30960 × 30972) / 12
LCM(30960,30972) = 958893120 / 12
LCM(30960,30972) = 79907760

Least Common Multiple (LCM) of 30960 and 30972 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30960 and 30972. First we will calculate the prime factors of 30960 and 30972.

Prime Factorization of 30960

Prime Factorization of 30972

Now multiplying the highest exponent prime factors to calculate the LCM of 30960 and 30972.

LCM(30960,30972) = 2⁴ × 3² × 5¹ × 43¹ × 29¹ × 89¹
LCM(30960,30972) = 79907760