What is the Least Common Multiple of 31872 and 31884?

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 31872 and 31884 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31872 and 31884, than apply into the LCM equation.

GCF(31872,31884) = 12
LCM(31872,31884) = ( 31872 × 31884) / 12
LCM(31872,31884) = 1016206848 / 12
LCM(31872,31884) = 84683904

Least Common Multiple (LCM) of 31872 and 31884 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31872 and 31884. First we will calculate the prime factors of 31872 and 31884.

Prime Factorization of 31872

Prime Factorization of 31884

Now multiplying the highest exponent prime factors to calculate the LCM of 31872 and 31884.

LCM(31872,31884) = 2⁷ × 3¹ × 83¹ × 2657¹
LCM(31872,31884) = 84683904