What is the Least Common Multiple of 16000 and 16009?

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 16000 and 16009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16000 and 16009, than apply into the LCM equation.

GCF(16000,16009) = 1
LCM(16000,16009) = ( 16000 × 16009) / 1
LCM(16000,16009) = 256144000 / 1
LCM(16000,16009) = 256144000

Least Common Multiple (LCM) of 16000 and 16009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 16000 and 16009. First we will calculate the prime factors of 16000 and 16009.

Prime Factorization of 16000

Prime Factorization of 16009

Now multiplying the highest exponent prime factors to calculate the LCM of 16000 and 16009.

LCM(16000,16009) = 2⁷ × 5³ × 7¹ × 2287¹
LCM(16000,16009) = 256144000