What is the Least Common Multiple of 17745 and 17754?

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 17745 and 17754 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17745 and 17754, than apply into the LCM equation.

GCF(17745,17754) = 3
LCM(17745,17754) = ( 17745 × 17754) / 3
LCM(17745,17754) = 315044730 / 3
LCM(17745,17754) = 105014910

Least Common Multiple (LCM) of 17745 and 17754 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17745 and 17754. First we will calculate the prime factors of 17745 and 17754.

Prime Factorization of 17745

Prime Factorization of 17754

Now multiplying the highest exponent prime factors to calculate the LCM of 17745 and 17754.

LCM(17745,17754) = 3¹ × 5¹ × 7¹ × 13² × 2¹ × 11¹ × 269¹
LCM(17745,17754) = 105014910