What is the Least Common Multiple of 5160 and 5175?

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 5160 and 5175 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5160 and 5175, than apply into the LCM equation.

GCF(5160,5175) = 15
LCM(5160,5175) = ( 5160 × 5175) / 15
LCM(5160,5175) = 26703000 / 15
LCM(5160,5175) = 1780200

Least Common Multiple (LCM) of 5160 and 5175 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5160 and 5175. First we will calculate the prime factors of 5160 and 5175.

Prime Factorization of 5160

Prime Factorization of 5175

Now multiplying the highest exponent prime factors to calculate the LCM of 5160 and 5175.

LCM(5160,5175) = 2³ × 3² × 5² × 43¹ × 23¹
LCM(5160,5175) = 1780200