What is the Least Common Multiple of 10509 and 10517?

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 10509 and 10517 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10509 and 10517, than apply into the LCM equation.

GCF(10509,10517) = 1
LCM(10509,10517) = ( 10509 × 10517) / 1
LCM(10509,10517) = 110523153 / 1
LCM(10509,10517) = 110523153

Least Common Multiple (LCM) of 10509 and 10517 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10509 and 10517. First we will calculate the prime factors of 10509 and 10517.

Prime Factorization of 10509

Prime Factorization of 10517

Now multiplying the highest exponent prime factors to calculate the LCM of 10509 and 10517.

LCM(10509,10517) = 3¹ × 31¹ × 113¹ × 13¹ × 809¹
LCM(10509,10517) = 110523153