What is the Least Common Multiple of 10512 and 10519?

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 10512 and 10519 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10512 and 10519, than apply into the LCM equation.

GCF(10512,10519) = 1
LCM(10512,10519) = ( 10512 × 10519) / 1
LCM(10512,10519) = 110575728 / 1
LCM(10512,10519) = 110575728

Least Common Multiple (LCM) of 10512 and 10519 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10512 and 10519. First we will calculate the prime factors of 10512 and 10519.

Prime Factorization of 10512

Prime Factorization of 10519

Now multiplying the highest exponent prime factors to calculate the LCM of 10512 and 10519.

LCM(10512,10519) = 2⁴ × 3² × 73¹ × 67¹ × 157¹
LCM(10512,10519) = 110575728