What is the Least Common Multiple of 69000 and 69012?

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 69000 and 69012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69000 and 69012, than apply into the LCM equation.

GCF(69000,69012) = 12
LCM(69000,69012) = ( 69000 × 69012) / 12
LCM(69000,69012) = 4761828000 / 12
LCM(69000,69012) = 396819000

Least Common Multiple (LCM) of 69000 and 69012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69000 and 69012. First we will calculate the prime factors of 69000 and 69012.

Prime Factorization of 69000

Prime Factorization of 69012

Now multiplying the highest exponent prime factors to calculate the LCM of 69000 and 69012.

LCM(69000,69012) = 2³ × 3⁵ × 5³ × 23¹ × 71¹
LCM(69000,69012) = 396819000