What is the Least Common Multiple of 17805 and 17824?

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 17805 and 17824 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17805 and 17824, than apply into the LCM equation.

GCF(17805,17824) = 1
LCM(17805,17824) = ( 17805 × 17824) / 1
LCM(17805,17824) = 317356320 / 1
LCM(17805,17824) = 317356320

Least Common Multiple (LCM) of 17805 and 17824 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17805 and 17824. First we will calculate the prime factors of 17805 and 17824.

Prime Factorization of 17805

Prime Factorization of 17824

Now multiplying the highest exponent prime factors to calculate the LCM of 17805 and 17824.

LCM(17805,17824) = 3¹ × 5¹ × 1187¹ × 2⁵ × 557¹
LCM(17805,17824) = 317356320