What is the Least Common Multiple of 14000 and 14008?

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 14000 and 14008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14000 and 14008, than apply into the LCM equation.

GCF(14000,14008) = 8
LCM(14000,14008) = ( 14000 × 14008) / 8
LCM(14000,14008) = 196112000 / 8
LCM(14000,14008) = 24514000

Least Common Multiple (LCM) of 14000 and 14008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14000 and 14008. First we will calculate the prime factors of 14000 and 14008.

Prime Factorization of 14000

Prime Factorization of 14008

Now multiplying the highest exponent prime factors to calculate the LCM of 14000 and 14008.

LCM(14000,14008) = 2⁴ × 5³ × 7¹ × 17¹ × 103¹
LCM(14000,14008) = 24514000