What is the Least Common Multiple of 71000 and 71008?

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 71000 and 71008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 71000 and 71008, than apply into the LCM equation.

GCF(71000,71008) = 8
LCM(71000,71008) = ( 71000 × 71008) / 8
LCM(71000,71008) = 5041568000 / 8
LCM(71000,71008) = 630196000

Least Common Multiple (LCM) of 71000 and 71008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 71000 and 71008. First we will calculate the prime factors of 71000 and 71008.

Prime Factorization of 71000

Prime Factorization of 71008

Now multiplying the highest exponent prime factors to calculate the LCM of 71000 and 71008.

LCM(71000,71008) = 2⁵ × 5³ × 71¹ × 7¹ × 317¹
LCM(71000,71008) = 630196000