What is the Least Common Multiple of 12960 and 12975?

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 12960 and 12975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12960 and 12975, than apply into the LCM equation.

GCF(12960,12975) = 15
LCM(12960,12975) = ( 12960 × 12975) / 15
LCM(12960,12975) = 168156000 / 15
LCM(12960,12975) = 11210400

Least Common Multiple (LCM) of 12960 and 12975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12960 and 12975. First we will calculate the prime factors of 12960 and 12975.

Prime Factorization of 12960

Prime Factorization of 12975

Now multiplying the highest exponent prime factors to calculate the LCM of 12960 and 12975.

LCM(12960,12975) = 2⁵ × 3⁴ × 5² × 173¹
LCM(12960,12975) = 11210400