What is the Least Common Multiple of 9684 and 9696?

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 9684 and 9696 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9684 and 9696, than apply into the LCM equation.

GCF(9684,9696) = 12
LCM(9684,9696) = ( 9684 × 9696) / 12
LCM(9684,9696) = 93896064 / 12
LCM(9684,9696) = 7824672

Least Common Multiple (LCM) of 9684 and 9696 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9684 and 9696. First we will calculate the prime factors of 9684 and 9696.

Prime Factorization of 9684

Prime Factorization of 9696

Now multiplying the highest exponent prime factors to calculate the LCM of 9684 and 9696.

LCM(9684,9696) = 2⁵ × 3² × 269¹ × 101¹
LCM(9684,9696) = 7824672