What is the Least Common Multiple of 76005 and 76020?

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 76005 and 76020 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 76005 and 76020, than apply into the LCM equation.

GCF(76005,76020) = 15
LCM(76005,76020) = ( 76005 × 76020) / 15
LCM(76005,76020) = 5777900100 / 15
LCM(76005,76020) = 385193340

Least Common Multiple (LCM) of 76005 and 76020 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76005 and 76020. First we will calculate the prime factors of 76005 and 76020.

Prime Factorization of 76005

Prime Factorization of 76020

Now multiplying the highest exponent prime factors to calculate the LCM of 76005 and 76020.

LCM(76005,76020) = 3³ × 5¹ × 563¹ × 2² × 7¹ × 181¹
LCM(76005,76020) = 385193340