What is the Least Common Multiple of 17808 and 17823?

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 17808 and 17823 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17808 and 17823, than apply into the LCM equation.

GCF(17808,17823) = 3
LCM(17808,17823) = ( 17808 × 17823) / 3
LCM(17808,17823) = 317391984 / 3
LCM(17808,17823) = 105797328

Least Common Multiple (LCM) of 17808 and 17823 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17808 and 17823. First we will calculate the prime factors of 17808 and 17823.

Prime Factorization of 17808

Prime Factorization of 17823

Now multiplying the highest exponent prime factors to calculate the LCM of 17808 and 17823.

LCM(17808,17823) = 2⁴ × 3¹ × 7¹ × 53¹ × 13¹ × 457¹
LCM(17808,17823) = 105797328