What is the Least Common Multiple of 30696 and 30705?

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 30696 and 30705 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30696 and 30705, than apply into the LCM equation.

GCF(30696,30705) = 3
LCM(30696,30705) = ( 30696 × 30705) / 3
LCM(30696,30705) = 942520680 / 3
LCM(30696,30705) = 314173560

Least Common Multiple (LCM) of 30696 and 30705 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30696 and 30705. First we will calculate the prime factors of 30696 and 30705.

Prime Factorization of 30696

Prime Factorization of 30705

Now multiplying the highest exponent prime factors to calculate the LCM of 30696 and 30705.

LCM(30696,30705) = 2³ × 3¹ × 1279¹ × 5¹ × 23¹ × 89¹
LCM(30696,30705) = 314173560