What is the Least Common Multiple of 31824 and 31830?

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 31824 and 31830 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31824 and 31830, than apply into the LCM equation.

GCF(31824,31830) = 6
LCM(31824,31830) = ( 31824 × 31830) / 6
LCM(31824,31830) = 1012957920 / 6
LCM(31824,31830) = 168826320

Least Common Multiple (LCM) of 31824 and 31830 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31824 and 31830. First we will calculate the prime factors of 31824 and 31830.

Prime Factorization of 31824

Prime Factorization of 31830

Now multiplying the highest exponent prime factors to calculate the LCM of 31824 and 31830.

LCM(31824,31830) = 2⁴ × 3² × 13¹ × 17¹ × 5¹ × 1061¹
LCM(31824,31830) = 168826320