What is the Least Common Multiple of 6960 and 6975?

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 6960 and 6975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6960 and 6975, than apply into the LCM equation.

GCF(6960,6975) = 15
LCM(6960,6975) = ( 6960 × 6975) / 15
LCM(6960,6975) = 48546000 / 15
LCM(6960,6975) = 3236400

Least Common Multiple (LCM) of 6960 and 6975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6960 and 6975. First we will calculate the prime factors of 6960 and 6975.

Prime Factorization of 6960

Prime Factorization of 6975

Now multiplying the highest exponent prime factors to calculate the LCM of 6960 and 6975.

LCM(6960,6975) = 2⁴ × 3² × 5² × 29¹ × 31¹
LCM(6960,6975) = 3236400