What is the Least Common Multiple of 17745 and 17757?

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 17757 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 17757, than apply into the LCM equation.

GCF(17745,17757) = 3
LCM(17745,17757) = ( 17745 × 17757) / 3
LCM(17745,17757) = 315097965 / 3
LCM(17745,17757) = 105032655

Least Common Multiple (LCM) of 17745 and 17757 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17745 and 17757. First we will calculate the prime factors of 17745 and 17757.

Prime Factorization of 17745

Prime Factorization of 17757

Now multiplying the highest exponent prime factors to calculate the LCM of 17745 and 17757.

LCM(17745,17757) = 3² × 5¹ × 7¹ × 13² × 1973¹
LCM(17745,17757) = 105032655