What is the Least Common Multiple of 9712 and 9724?

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 9712 and 9724 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9712 and 9724, than apply into the LCM equation.

GCF(9712,9724) = 4
LCM(9712,9724) = ( 9712 × 9724) / 4
LCM(9712,9724) = 94439488 / 4
LCM(9712,9724) = 23609872

Least Common Multiple (LCM) of 9712 and 9724 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9712 and 9724. First we will calculate the prime factors of 9712 and 9724.

Prime Factorization of 9712

Prime Factorization of 9724

Now multiplying the highest exponent prime factors to calculate the LCM of 9712 and 9724.

LCM(9712,9724) = 2⁴ × 607¹ × 11¹ × 13¹ × 17¹
LCM(9712,9724) = 23609872