What is the Least Common Multiple of 9705 and 9723?

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 9705 and 9723 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9705 and 9723, than apply into the LCM equation.

GCF(9705,9723) = 3
LCM(9705,9723) = ( 9705 × 9723) / 3
LCM(9705,9723) = 94361715 / 3
LCM(9705,9723) = 31453905

Least Common Multiple (LCM) of 9705 and 9723 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9705 and 9723. First we will calculate the prime factors of 9705 and 9723.

Prime Factorization of 9705

Prime Factorization of 9723

Now multiplying the highest exponent prime factors to calculate the LCM of 9705 and 9723.

LCM(9705,9723) = 3¹ × 5¹ × 647¹ × 7¹ × 463¹
LCM(9705,9723) = 31453905