What is the Least Common Multiple of 46494 and 46500?

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 46494 and 46500 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 46494 and 46500, than apply into the LCM equation.

GCF(46494,46500) = 6
LCM(46494,46500) = ( 46494 × 46500) / 6
LCM(46494,46500) = 2161971000 / 6
LCM(46494,46500) = 360328500

Least Common Multiple (LCM) of 46494 and 46500 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 46494 and 46500. First we will calculate the prime factors of 46494 and 46500.

Prime Factorization of 46494

Prime Factorization of 46500

Now multiplying the highest exponent prime factors to calculate the LCM of 46494 and 46500.

LCM(46494,46500) = 2² × 3⁴ × 7¹ × 41¹ × 5³ × 31¹
LCM(46494,46500) = 360328500