What is the Least Common Multiple of 8000 and 8009?

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 8000 and 8009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8000 and 8009, than apply into the LCM equation.

GCF(8000,8009) = 1
LCM(8000,8009) = ( 8000 × 8009) / 1
LCM(8000,8009) = 64072000 / 1
LCM(8000,8009) = 64072000

Least Common Multiple (LCM) of 8000 and 8009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8000 and 8009. First we will calculate the prime factors of 8000 and 8009.

Prime Factorization of 8000

Prime Factorization of 8009

Now multiplying the highest exponent prime factors to calculate the LCM of 8000 and 8009.

LCM(8000,8009) = 2⁶ × 5³ × 8009¹
LCM(8000,8009) = 64072000