What is the Least Common Multiple of 81984 and 82000?

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 81984 and 82000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 81984 and 82000, than apply into the LCM equation.

GCF(81984,82000) = 16
LCM(81984,82000) = ( 81984 × 82000) / 16
LCM(81984,82000) = 6722688000 / 16
LCM(81984,82000) = 420168000

Least Common Multiple (LCM) of 81984 and 82000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 81984 and 82000. First we will calculate the prime factors of 81984 and 82000.

Prime Factorization of 81984

Prime Factorization of 82000

Now multiplying the highest exponent prime factors to calculate the LCM of 81984 and 82000.

LCM(81984,82000) = 2⁶ × 3¹ × 7¹ × 61¹ × 5³ × 41¹
LCM(81984,82000) = 420168000