What is the Least Common Multiple of 31808 and 31822?

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 31808 and 31822 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31808 and 31822, than apply into the LCM equation.

GCF(31808,31822) = 14
LCM(31808,31822) = ( 31808 × 31822) / 14
LCM(31808,31822) = 1012194176 / 14
LCM(31808,31822) = 72299584

Least Common Multiple (LCM) of 31808 and 31822 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31808 and 31822. First we will calculate the prime factors of 31808 and 31822.

Prime Factorization of 31808

Prime Factorization of 31822

Now multiplying the highest exponent prime factors to calculate the LCM of 31808 and 31822.

LCM(31808,31822) = 2⁶ × 7¹ × 71¹ × 2273¹
LCM(31808,31822) = 72299584