What is the Least Common Multiple of 31374 and 31392?

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 31374 and 31392 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31374 and 31392, than apply into the LCM equation.

GCF(31374,31392) = 18
LCM(31374,31392) = ( 31374 × 31392) / 18
LCM(31374,31392) = 984892608 / 18
LCM(31374,31392) = 54716256

Least Common Multiple (LCM) of 31374 and 31392 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31374 and 31392. First we will calculate the prime factors of 31374 and 31392.

Prime Factorization of 31374

Prime Factorization of 31392

Now multiplying the highest exponent prime factors to calculate the LCM of 31374 and 31392.

LCM(31374,31392) = 2⁵ × 3³ × 7¹ × 83¹ × 109¹
LCM(31374,31392) = 54716256