What is the Least Common Multiple of 17696 and 17705?

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 17696 and 17705 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17696 and 17705, than apply into the LCM equation.

GCF(17696,17705) = 1
LCM(17696,17705) = ( 17696 × 17705) / 1
LCM(17696,17705) = 313307680 / 1
LCM(17696,17705) = 313307680

Least Common Multiple (LCM) of 17696 and 17705 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17696 and 17705. First we will calculate the prime factors of 17696 and 17705.

Prime Factorization of 17696

Prime Factorization of 17705

Now multiplying the highest exponent prime factors to calculate the LCM of 17696 and 17705.

LCM(17696,17705) = 2⁵ × 7¹ × 79¹ × 5¹ × 3541¹
LCM(17696,17705) = 313307680