What is the Least Common Multiple of 84000 and 84009?

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 84000 and 84009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 84000 and 84009, than apply into the LCM equation.

GCF(84000,84009) = 3
LCM(84000,84009) = ( 84000 × 84009) / 3
LCM(84000,84009) = 7056756000 / 3
LCM(84000,84009) = 2352252000

Least Common Multiple (LCM) of 84000 and 84009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 84000 and 84009. First we will calculate the prime factors of 84000 and 84009.

Prime Factorization of 84000

Prime Factorization of 84009

Now multiplying the highest exponent prime factors to calculate the LCM of 84000 and 84009.

LCM(84000,84009) = 2⁵ × 3¹ × 5³ × 7¹ × 41¹ × 683¹
LCM(84000,84009) = 2352252000