What is the Least Common Multiple of 2160 and 2175?

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 2160 and 2175 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2160 and 2175, than apply into the LCM equation.

GCF(2160,2175) = 15
LCM(2160,2175) = ( 2160 × 2175) / 15
LCM(2160,2175) = 4698000 / 15
LCM(2160,2175) = 313200

Least Common Multiple (LCM) of 2160 and 2175 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2160 and 2175. First we will calculate the prime factors of 2160 and 2175.

Prime Factorization of 2160

Prime Factorization of 2175

Now multiplying the highest exponent prime factors to calculate the LCM of 2160 and 2175.

LCM(2160,2175) = 2⁴ × 3³ × 5² × 29¹
LCM(2160,2175) = 313200