What is the Least Common Multiple of 31688 and 31705?

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 31688 and 31705 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31688 and 31705, than apply into the LCM equation.

GCF(31688,31705) = 17
LCM(31688,31705) = ( 31688 × 31705) / 17
LCM(31688,31705) = 1004668040 / 17
LCM(31688,31705) = 59098120

Least Common Multiple (LCM) of 31688 and 31705 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31688 and 31705. First we will calculate the prime factors of 31688 and 31705.

Prime Factorization of 31688

Prime Factorization of 31705

Now multiplying the highest exponent prime factors to calculate the LCM of 31688 and 31705.

LCM(31688,31705) = 2³ × 17¹ × 233¹ × 5¹ × 373¹
LCM(31688,31705) = 59098120