What is the Least Common Multiple of 2000 and 2014?

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 2000 and 2014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2000 and 2014, than apply into the LCM equation.

GCF(2000,2014) = 2
LCM(2000,2014) = ( 2000 × 2014) / 2
LCM(2000,2014) = 4028000 / 2
LCM(2000,2014) = 2014000

Least Common Multiple (LCM) of 2000 and 2014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2000 and 2014. First we will calculate the prime factors of 2000 and 2014.

Prime Factorization of 2000

Prime Factorization of 2014

Now multiplying the highest exponent prime factors to calculate the LCM of 2000 and 2014.

LCM(2000,2014) = 2⁴ × 5³ × 19¹ × 53¹
LCM(2000,2014) = 2014000