What is the Least Common Multiple of 10509 and 10513?

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 10513 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 10513, than apply into the LCM equation.

GCF(10509,10513) = 1
LCM(10509,10513) = ( 10509 × 10513) / 1
LCM(10509,10513) = 110481117 / 1
LCM(10509,10513) = 110481117

Least Common Multiple (LCM) of 10509 and 10513 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10509 and 10513. First we will calculate the prime factors of 10509 and 10513.

Prime Factorization of 10509

Prime Factorization of 10513

Now multiplying the highest exponent prime factors to calculate the LCM of 10509 and 10513.

LCM(10509,10513) = 3¹ × 31¹ × 113¹ × 10513¹
LCM(10509,10513) = 110481117