What is the Least Common Multiple of 42000 and 42009?

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 42000 and 42009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42000 and 42009, than apply into the LCM equation.

GCF(42000,42009) = 3
LCM(42000,42009) = ( 42000 × 42009) / 3
LCM(42000,42009) = 1764378000 / 3
LCM(42000,42009) = 588126000

Least Common Multiple (LCM) of 42000 and 42009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42000 and 42009. First we will calculate the prime factors of 42000 and 42009.

Prime Factorization of 42000

Prime Factorization of 42009

Now multiplying the highest exponent prime factors to calculate the LCM of 42000 and 42009.

LCM(42000,42009) = 2⁴ × 3¹ × 5³ × 7¹ × 11¹ × 19¹ × 67¹
LCM(42000,42009) = 588126000