What is the Least Common Multiple of 9708 and 9714?

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 9708 and 9714 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9708 and 9714, than apply into the LCM equation.

GCF(9708,9714) = 6
LCM(9708,9714) = ( 9708 × 9714) / 6
LCM(9708,9714) = 94303512 / 6
LCM(9708,9714) = 15717252

Least Common Multiple (LCM) of 9708 and 9714 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9708 and 9714. First we will calculate the prime factors of 9708 and 9714.

Prime Factorization of 9708

Prime Factorization of 9714

Now multiplying the highest exponent prime factors to calculate the LCM of 9708 and 9714.

LCM(9708,9714) = 2² × 3¹ × 809¹ × 1619¹
LCM(9708,9714) = 15717252