What is the Least Common Multiple of 14688 and 14705?

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 14688 and 14705 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14688 and 14705, than apply into the LCM equation.

GCF(14688,14705) = 17
LCM(14688,14705) = ( 14688 × 14705) / 17
LCM(14688,14705) = 215987040 / 17
LCM(14688,14705) = 12705120

Least Common Multiple (LCM) of 14688 and 14705 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14688 and 14705. First we will calculate the prime factors of 14688 and 14705.

Prime Factorization of 14688

Prime Factorization of 14705

Now multiplying the highest exponent prime factors to calculate the LCM of 14688 and 14705.

LCM(14688,14705) = 2⁵ × 3³ × 17¹ × 5¹ × 173¹
LCM(14688,14705) = 12705120