What is the Least Common Multiple of 9729 and 9744?

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 9729 and 9744 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9729 and 9744, than apply into the LCM equation.

GCF(9729,9744) = 3
LCM(9729,9744) = ( 9729 × 9744) / 3
LCM(9729,9744) = 94799376 / 3
LCM(9729,9744) = 31599792

Least Common Multiple (LCM) of 9729 and 9744 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9729 and 9744. First we will calculate the prime factors of 9729 and 9744.

Prime Factorization of 9729

Prime Factorization of 9744

Now multiplying the highest exponent prime factors to calculate the LCM of 9729 and 9744.

LCM(9729,9744) = 3² × 23¹ × 47¹ × 2⁴ × 7¹ × 29¹
LCM(9729,9744) = 31599792