What is the Least Common Multiple of 42009 and 42024?

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 42009 and 42024 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42009 and 42024, than apply into the LCM equation.

GCF(42009,42024) = 3
LCM(42009,42024) = ( 42009 × 42024) / 3
LCM(42009,42024) = 1765386216 / 3
LCM(42009,42024) = 588462072

Least Common Multiple (LCM) of 42009 and 42024 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42009 and 42024. First we will calculate the prime factors of 42009 and 42024.

Prime Factorization of 42009

Prime Factorization of 42024

Now multiplying the highest exponent prime factors to calculate the LCM of 42009 and 42024.

LCM(42009,42024) = 3¹ × 11¹ × 19¹ × 67¹ × 2³ × 17¹ × 103¹
LCM(42009,42024) = 588462072