What is the Least Common Multiple of 34000 and 34014?

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 34000 and 34014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34000 and 34014, than apply into the LCM equation.

GCF(34000,34014) = 2
LCM(34000,34014) = ( 34000 × 34014) / 2
LCM(34000,34014) = 1156476000 / 2
LCM(34000,34014) = 578238000

Least Common Multiple (LCM) of 34000 and 34014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34000 and 34014. First we will calculate the prime factors of 34000 and 34014.

Prime Factorization of 34000

Prime Factorization of 34014

Now multiplying the highest exponent prime factors to calculate the LCM of 34000 and 34014.

LCM(34000,34014) = 2⁴ × 5³ × 17¹ × 3¹ × 5669¹
LCM(34000,34014) = 578238000