What is the Least Common Multiple of 17676 and 17696?

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 17676 and 17696 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17676 and 17696, than apply into the LCM equation.

GCF(17676,17696) = 4
LCM(17676,17696) = ( 17676 × 17696) / 4
LCM(17676,17696) = 312794496 / 4
LCM(17676,17696) = 78198624

Least Common Multiple (LCM) of 17676 and 17696 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17676 and 17696. First we will calculate the prime factors of 17676 and 17696.

Prime Factorization of 17676

Prime Factorization of 17696

Now multiplying the highest exponent prime factors to calculate the LCM of 17676 and 17696.

LCM(17676,17696) = 2⁵ × 3² × 491¹ × 7¹ × 79¹
LCM(17676,17696) = 78198624