What is the Least Common Multiple of 45984 and 46000?

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 45984 and 46000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45984 and 46000, than apply into the LCM equation.

GCF(45984,46000) = 16
LCM(45984,46000) = ( 45984 × 46000) / 16
LCM(45984,46000) = 2115264000 / 16
LCM(45984,46000) = 132204000

Least Common Multiple (LCM) of 45984 and 46000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45984 and 46000. First we will calculate the prime factors of 45984 and 46000.

Prime Factorization of 45984

Prime Factorization of 46000

Now multiplying the highest exponent prime factors to calculate the LCM of 45984 and 46000.

LCM(45984,46000) = 2⁵ × 3¹ × 479¹ × 5³ × 23¹
LCM(45984,46000) = 132204000