What is the Least Common Multiple of 3960 and 3975?

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 3960 and 3975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3960 and 3975, than apply into the LCM equation.

GCF(3960,3975) = 15
LCM(3960,3975) = ( 3960 × 3975) / 15
LCM(3960,3975) = 15741000 / 15
LCM(3960,3975) = 1049400

Least Common Multiple (LCM) of 3960 and 3975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3960 and 3975. First we will calculate the prime factors of 3960 and 3975.

Prime Factorization of 3960

Prime Factorization of 3975

Now multiplying the highest exponent prime factors to calculate the LCM of 3960 and 3975.

LCM(3960,3975) = 2³ × 3² × 5² × 11¹ × 53¹
LCM(3960,3975) = 1049400