What is the Least Common Multiple of 31320 and 31335?

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 31320 and 31335 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31320 and 31335, than apply into the LCM equation.

GCF(31320,31335) = 15
LCM(31320,31335) = ( 31320 × 31335) / 15
LCM(31320,31335) = 981412200 / 15
LCM(31320,31335) = 65427480

Least Common Multiple (LCM) of 31320 and 31335 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31320 and 31335. First we will calculate the prime factors of 31320 and 31335.

Prime Factorization of 31320

Prime Factorization of 31335

Now multiplying the highest exponent prime factors to calculate the LCM of 31320 and 31335.

LCM(31320,31335) = 2³ × 3³ × 5¹ × 29¹ × 2089¹
LCM(31320,31335) = 65427480