What is the Least Common Multiple of 34000 and 34007?

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 34007 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 34007, than apply into the LCM equation.

GCF(34000,34007) = 1
LCM(34000,34007) = ( 34000 × 34007) / 1
LCM(34000,34007) = 1156238000 / 1
LCM(34000,34007) = 1156238000

Least Common Multiple (LCM) of 34000 and 34007 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34000 and 34007. First we will calculate the prime factors of 34000 and 34007.

Prime Factorization of 34000

Prime Factorization of 34007

Now multiplying the highest exponent prime factors to calculate the LCM of 34000 and 34007.

LCM(34000,34007) = 2⁴ × 5³ × 17¹ × 31¹ × 1097¹
LCM(34000,34007) = 1156238000