What is the Least Common Multiple of 9696 and 9708?

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 9696 and 9708 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9696 and 9708, than apply into the LCM equation.

GCF(9696,9708) = 12
LCM(9696,9708) = ( 9696 × 9708) / 12
LCM(9696,9708) = 94128768 / 12
LCM(9696,9708) = 7844064

Least Common Multiple (LCM) of 9696 and 9708 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9696 and 9708. First we will calculate the prime factors of 9696 and 9708.

Prime Factorization of 9696

Prime Factorization of 9708

Now multiplying the highest exponent prime factors to calculate the LCM of 9696 and 9708.

LCM(9696,9708) = 2⁵ × 3¹ × 101¹ × 809¹
LCM(9696,9708) = 7844064