What is the Least Common Multiple of 32000 and 32014?

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 32000 and 32014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32000 and 32014, than apply into the LCM equation.

GCF(32000,32014) = 2
LCM(32000,32014) = ( 32000 × 32014) / 2
LCM(32000,32014) = 1024448000 / 2
LCM(32000,32014) = 512224000

Least Common Multiple (LCM) of 32000 and 32014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32000 and 32014. First we will calculate the prime factors of 32000 and 32014.

Prime Factorization of 32000

Prime Factorization of 32014

Now multiplying the highest exponent prime factors to calculate the LCM of 32000 and 32014.

LCM(32000,32014) = 2⁸ × 5³ × 16007¹
LCM(32000,32014) = 512224000