What is the Least Common Multiple of 96096 and 96109?

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 96096 and 96109 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 96096 and 96109, than apply into the LCM equation.

GCF(96096,96109) = 13
LCM(96096,96109) = ( 96096 × 96109) / 13
LCM(96096,96109) = 9235690464 / 13
LCM(96096,96109) = 710437728

Least Common Multiple (LCM) of 96096 and 96109 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 96096 and 96109. First we will calculate the prime factors of 96096 and 96109.

Prime Factorization of 96096

Prime Factorization of 96109

Now multiplying the highest exponent prime factors to calculate the LCM of 96096 and 96109.

LCM(96096,96109) = 2⁵ × 3¹ × 7¹ × 11¹ × 13¹ × 7393¹
LCM(96096,96109) = 710437728