What is the Least Common Multiple of 14160 and 14175?

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 14160 and 14175 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14160 and 14175, than apply into the LCM equation.

GCF(14160,14175) = 15
LCM(14160,14175) = ( 14160 × 14175) / 15
LCM(14160,14175) = 200718000 / 15
LCM(14160,14175) = 13381200

Least Common Multiple (LCM) of 14160 and 14175 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14160 and 14175. First we will calculate the prime factors of 14160 and 14175.

Prime Factorization of 14160

Prime Factorization of 14175

Now multiplying the highest exponent prime factors to calculate the LCM of 14160 and 14175.

LCM(14160,14175) = 2⁴ × 3⁴ × 5² × 59¹ × 7¹
LCM(14160,14175) = 13381200