What is the Least Common Multiple of 76000 and 76009?

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 76009 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 76009, than apply into the LCM equation.

GCF(76000,76009) = 1
LCM(76000,76009) = ( 76000 × 76009) / 1
LCM(76000,76009) = 5776684000 / 1
LCM(76000,76009) = 5776684000

Least Common Multiple (LCM) of 76000 and 76009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76000 and 76009. First we will calculate the prime factors of 76000 and 76009.

Prime Factorization of 76000

Prime Factorization of 76009

Now multiplying the highest exponent prime factors to calculate the LCM of 76000 and 76009.

LCM(76000,76009) = 2⁵ × 5³ × 19¹ × 29¹ × 2621¹
LCM(76000,76009) = 5776684000