What is the Least Common Multiple of 15984 and 16000?

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 15984 and 16000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15984 and 16000, than apply into the LCM equation.

GCF(15984,16000) = 16
LCM(15984,16000) = ( 15984 × 16000) / 16
LCM(15984,16000) = 255744000 / 16
LCM(15984,16000) = 15984000

Least Common Multiple (LCM) of 15984 and 16000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 15984 and 16000. First we will calculate the prime factors of 15984 and 16000.

Prime Factorization of 15984

Prime Factorization of 16000

Now multiplying the highest exponent prime factors to calculate the LCM of 15984 and 16000.

LCM(15984,16000) = 2⁷ × 3³ × 37¹ × 5³
LCM(15984,16000) = 15984000