What is the Least Common Multiple of 76080 and 76096?

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 76080 and 76096 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 76080 and 76096, than apply into the LCM equation.

GCF(76080,76096) = 16
LCM(76080,76096) = ( 76080 × 76096) / 16
LCM(76080,76096) = 5789383680 / 16
LCM(76080,76096) = 361836480

Least Common Multiple (LCM) of 76080 and 76096 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76080 and 76096. First we will calculate the prime factors of 76080 and 76096.

Prime Factorization of 76080

Prime Factorization of 76096

Now multiplying the highest exponent prime factors to calculate the LCM of 76080 and 76096.

LCM(76080,76096) = 2⁶ × 3¹ × 5¹ × 317¹ × 29¹ × 41¹
LCM(76080,76096) = 361836480