What is the Least Common Multiple of 90000 and 90009?

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 90000 and 90009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90000 and 90009, than apply into the LCM equation.

GCF(90000,90009) = 9
LCM(90000,90009) = ( 90000 × 90009) / 9
LCM(90000,90009) = 8100810000 / 9
LCM(90000,90009) = 900090000

Least Common Multiple (LCM) of 90000 and 90009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90000 and 90009. First we will calculate the prime factors of 90000 and 90009.

Prime Factorization of 90000

Prime Factorization of 90009

Now multiplying the highest exponent prime factors to calculate the LCM of 90000 and 90009.

LCM(90000,90009) = 2⁴ × 3² × 5⁴ × 73¹ × 137¹
LCM(90000,90009) = 900090000