What is the Least Common Multiple of 51984 and 52000?

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 51984 and 52000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51984 and 52000, than apply into the LCM equation.

GCF(51984,52000) = 16
LCM(51984,52000) = ( 51984 × 52000) / 16
LCM(51984,52000) = 2703168000 / 16
LCM(51984,52000) = 168948000

Least Common Multiple (LCM) of 51984 and 52000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51984 and 52000. First we will calculate the prime factors of 51984 and 52000.

Prime Factorization of 51984

Prime Factorization of 52000

Now multiplying the highest exponent prime factors to calculate the LCM of 51984 and 52000.

LCM(51984,52000) = 2⁵ × 3² × 19² × 5³ × 13¹
LCM(51984,52000) = 168948000