What is the Least Common Multiple of 9720 and 9729?

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 9720 and 9729 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9720 and 9729, than apply into the LCM equation.

GCF(9720,9729) = 9
LCM(9720,9729) = ( 9720 × 9729) / 9
LCM(9720,9729) = 94565880 / 9
LCM(9720,9729) = 10507320

Least Common Multiple (LCM) of 9720 and 9729 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9720 and 9729. First we will calculate the prime factors of 9720 and 9729.

Prime Factorization of 9720

Prime Factorization of 9729

Now multiplying the highest exponent prime factors to calculate the LCM of 9720 and 9729.

LCM(9720,9729) = 2³ × 3⁵ × 5¹ × 23¹ × 47¹
LCM(9720,9729) = 10507320