What is the Least Common Multiple of 36960 and 36975?

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 36960 and 36975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 36960 and 36975, than apply into the LCM equation.

GCF(36960,36975) = 15
LCM(36960,36975) = ( 36960 × 36975) / 15
LCM(36960,36975) = 1366596000 / 15
LCM(36960,36975) = 91106400

Least Common Multiple (LCM) of 36960 and 36975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 36960 and 36975. First we will calculate the prime factors of 36960 and 36975.

Prime Factorization of 36960

Prime Factorization of 36975

Now multiplying the highest exponent prime factors to calculate the LCM of 36960 and 36975.

LCM(36960,36975) = 2⁵ × 3¹ × 5² × 7¹ × 11¹ × 17¹ × 29¹
LCM(36960,36975) = 91106400