What is the Least Common Multiple of 16000 and 16008?

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 16008 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 16008, than apply into the LCM equation.

GCF(16000,16008) = 8
LCM(16000,16008) = ( 16000 × 16008) / 8
LCM(16000,16008) = 256128000 / 8
LCM(16000,16008) = 32016000

Least Common Multiple (LCM) of 16000 and 16008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 16000 and 16008. First we will calculate the prime factors of 16000 and 16008.

Prime Factorization of 16000

Prime Factorization of 16008

Now multiplying the highest exponent prime factors to calculate the LCM of 16000 and 16008.

LCM(16000,16008) = 2⁷ × 5³ × 3¹ × 23¹ × 29¹
LCM(16000,16008) = 32016000