What is the Least Common Multiple of 10500 and 10512?

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 10500 and 10512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10500 and 10512, than apply into the LCM equation.

GCF(10500,10512) = 12
LCM(10500,10512) = ( 10500 × 10512) / 12
LCM(10500,10512) = 110376000 / 12
LCM(10500,10512) = 9198000

Least Common Multiple (LCM) of 10500 and 10512 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10500 and 10512. First we will calculate the prime factors of 10500 and 10512.

Prime Factorization of 10500

Prime Factorization of 10512

Now multiplying the highest exponent prime factors to calculate the LCM of 10500 and 10512.

LCM(10500,10512) = 2⁴ × 3² × 5³ × 7¹ × 73¹
LCM(10500,10512) = 9198000