What is the Least Common Multiple of 24000 and 24009?

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 24000 and 24009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 24000 and 24009, than apply into the LCM equation.

GCF(24000,24009) = 3
LCM(24000,24009) = ( 24000 × 24009) / 3
LCM(24000,24009) = 576216000 / 3
LCM(24000,24009) = 192072000

Least Common Multiple (LCM) of 24000 and 24009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 24000 and 24009. First we will calculate the prime factors of 24000 and 24009.

Prime Factorization of 24000

Prime Factorization of 24009

Now multiplying the highest exponent prime factors to calculate the LCM of 24000 and 24009.

LCM(24000,24009) = 2⁶ × 3¹ × 5³ × 53¹ × 151¹
LCM(24000,24009) = 192072000