What is the Least Common Multiple of 16500 and 16512?

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 16500 and 16512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16500 and 16512, than apply into the LCM equation.

GCF(16500,16512) = 12
LCM(16500,16512) = ( 16500 × 16512) / 12
LCM(16500,16512) = 272448000 / 12
LCM(16500,16512) = 22704000

Least Common Multiple (LCM) of 16500 and 16512 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 16500 and 16512. First we will calculate the prime factors of 16500 and 16512.

Prime Factorization of 16500

Prime Factorization of 16512

Now multiplying the highest exponent prime factors to calculate the LCM of 16500 and 16512.

LCM(16500,16512) = 2⁷ × 3¹ × 5³ × 11¹ × 43¹
LCM(16500,16512) = 22704000