What is the Least Common Multiple of 31575 and 31584?

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 31575 and 31584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31575 and 31584, than apply into the LCM equation.

GCF(31575,31584) = 3
LCM(31575,31584) = ( 31575 × 31584) / 3
LCM(31575,31584) = 997264800 / 3
LCM(31575,31584) = 332421600

Least Common Multiple (LCM) of 31575 and 31584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31575 and 31584. First we will calculate the prime factors of 31575 and 31584.

Prime Factorization of 31575

Prime Factorization of 31584

Now multiplying the highest exponent prime factors to calculate the LCM of 31575 and 31584.

LCM(31575,31584) = 3¹ × 5² × 421¹ × 2⁵ × 7¹ × 47¹
LCM(31575,31584) = 332421600