What is the Least Common Multiple of 76000 and 76015?

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 76000 and 76015 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 76000 and 76015, than apply into the LCM equation.

GCF(76000,76015) = 5
LCM(76000,76015) = ( 76000 × 76015) / 5
LCM(76000,76015) = 5777140000 / 5
LCM(76000,76015) = 1155428000

Least Common Multiple (LCM) of 76000 and 76015 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76000 and 76015. First we will calculate the prime factors of 76000 and 76015.

Prime Factorization of 76000

Prime Factorization of 76015

Now multiplying the highest exponent prime factors to calculate the LCM of 76000 and 76015.

LCM(76000,76015) = 2⁵ × 5³ × 19¹ × 23¹ × 661¹
LCM(76000,76015) = 1155428000