What is the Least Common Multiple of 28000 and 28014?

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 28000 and 28014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 28000 and 28014, than apply into the LCM equation.

GCF(28000,28014) = 14
LCM(28000,28014) = ( 28000 × 28014) / 14
LCM(28000,28014) = 784392000 / 14
LCM(28000,28014) = 56028000

Least Common Multiple (LCM) of 28000 and 28014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 28000 and 28014. First we will calculate the prime factors of 28000 and 28014.

Prime Factorization of 28000

Prime Factorization of 28014

Now multiplying the highest exponent prime factors to calculate the LCM of 28000 and 28014.

LCM(28000,28014) = 2⁵ × 5³ × 7¹ × 3¹ × 23¹ × 29¹
LCM(28000,28014) = 56028000