What is the Least Common Multiple of 10523 and 10538?

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 10523 and 10538 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10523 and 10538, than apply into the LCM equation.

GCF(10523,10538) = 1
LCM(10523,10538) = ( 10523 × 10538) / 1
LCM(10523,10538) = 110891374 / 1
LCM(10523,10538) = 110891374

Least Common Multiple (LCM) of 10523 and 10538 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10523 and 10538. First we will calculate the prime factors of 10523 and 10538.

Prime Factorization of 10523

Prime Factorization of 10538

Now multiplying the highest exponent prime factors to calculate the LCM of 10523 and 10538.

LCM(10523,10538) = 17¹ × 619¹ × 2¹ × 11¹ × 479¹
LCM(10523,10538) = 110891374