What is the Least Common Multiple of 17696 and 17714?

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 17714 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 17714, than apply into the LCM equation.

GCF(17696,17714) = 2
LCM(17696,17714) = ( 17696 × 17714) / 2
LCM(17696,17714) = 313466944 / 2
LCM(17696,17714) = 156733472

Least Common Multiple (LCM) of 17696 and 17714 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17696 and 17714. First we will calculate the prime factors of 17696 and 17714.

Prime Factorization of 17696

Prime Factorization of 17714

Now multiplying the highest exponent prime factors to calculate the LCM of 17696 and 17714.

LCM(17696,17714) = 2⁵ × 7¹ × 79¹ × 17¹ × 521¹
LCM(17696,17714) = 156733472