What is the Least Common Multiple of 78096 and 78100?

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 78100 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 78100, than apply into the LCM equation.

GCF(78096,78100) = 4
LCM(78096,78100) = ( 78096 × 78100) / 4
LCM(78096,78100) = 6099297600 / 4
LCM(78096,78100) = 1524824400

Least Common Multiple (LCM) of 78096 and 78100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78096 and 78100. First we will calculate the prime factors of 78096 and 78100.

Prime Factorization of 78096

Prime Factorization of 78100

Now multiplying the highest exponent prime factors to calculate the LCM of 78096 and 78100.

LCM(78096,78100) = 2⁴ × 3¹ × 1627¹ × 5² × 11¹ × 71¹
LCM(78096,78100) = 1524824400