What is the Least Common Multiple of 66000 and 66009?

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 66000 and 66009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 66000 and 66009, than apply into the LCM equation.

GCF(66000,66009) = 3
LCM(66000,66009) = ( 66000 × 66009) / 3
LCM(66000,66009) = 4356594000 / 3
LCM(66000,66009) = 1452198000

Least Common Multiple (LCM) of 66000 and 66009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 66000 and 66009. First we will calculate the prime factors of 66000 and 66009.

Prime Factorization of 66000

Prime Factorization of 66009

Now multiplying the highest exponent prime factors to calculate the LCM of 66000 and 66009.

LCM(66000,66009) = 2⁴ × 3¹ × 5³ × 11¹ × 22003¹
LCM(66000,66009) = 1452198000