What is the Least Common Multiple of 7000 and 7014?

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 7000 and 7014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7000 and 7014, than apply into the LCM equation.

GCF(7000,7014) = 14
LCM(7000,7014) = ( 7000 × 7014) / 14
LCM(7000,7014) = 49098000 / 14
LCM(7000,7014) = 3507000

Least Common Multiple (LCM) of 7000 and 7014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7000 and 7014. First we will calculate the prime factors of 7000 and 7014.

Prime Factorization of 7000

Prime Factorization of 7014

Now multiplying the highest exponent prime factors to calculate the LCM of 7000 and 7014.

LCM(7000,7014) = 2³ × 5³ × 7¹ × 3¹ × 167¹
LCM(7000,7014) = 3507000