What is the Least Common Multiple of 9714 and 9728?

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 9714 and 9728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9714 and 9728, than apply into the LCM equation.

GCF(9714,9728) = 2
LCM(9714,9728) = ( 9714 × 9728) / 2
LCM(9714,9728) = 94497792 / 2
LCM(9714,9728) = 47248896

Least Common Multiple (LCM) of 9714 and 9728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9714 and 9728. First we will calculate the prime factors of 9714 and 9728.

Prime Factorization of 9714

Prime Factorization of 9728

Now multiplying the highest exponent prime factors to calculate the LCM of 9714 and 9728.

LCM(9714,9728) = 2⁹ × 3¹ × 1619¹ × 19¹
LCM(9714,9728) = 47248896