What is the Least Common Multiple of 78096 and 78112?

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 78096 and 78112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78096 and 78112, than apply into the LCM equation.

GCF(78096,78112) = 16
LCM(78096,78112) = ( 78096 × 78112) / 16
LCM(78096,78112) = 6100234752 / 16
LCM(78096,78112) = 381264672

Least Common Multiple (LCM) of 78096 and 78112 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78096 and 78112. First we will calculate the prime factors of 78096 and 78112.

Prime Factorization of 78096

Prime Factorization of 78112

Now multiplying the highest exponent prime factors to calculate the LCM of 78096 and 78112.

LCM(78096,78112) = 2⁵ × 3¹ × 1627¹ × 2441¹
LCM(78096,78112) = 381264672