What is the Least Common Multiple of 17544 and 17564?

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 17544 and 17564 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17544 and 17564, than apply into the LCM equation.

GCF(17544,17564) = 4
LCM(17544,17564) = ( 17544 × 17564) / 4
LCM(17544,17564) = 308142816 / 4
LCM(17544,17564) = 77035704

Least Common Multiple (LCM) of 17544 and 17564 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17544 and 17564. First we will calculate the prime factors of 17544 and 17564.

Prime Factorization of 17544

Prime Factorization of 17564

Now multiplying the highest exponent prime factors to calculate the LCM of 17544 and 17564.

LCM(17544,17564) = 2³ × 3¹ × 17¹ × 43¹ × 4391¹
LCM(17544,17564) = 77035704