What is the Least Common Multiple of 16560 and 16575?

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 16560 and 16575 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16560 and 16575, than apply into the LCM equation.

GCF(16560,16575) = 15
LCM(16560,16575) = ( 16560 × 16575) / 15
LCM(16560,16575) = 274482000 / 15
LCM(16560,16575) = 18298800

Least Common Multiple (LCM) of 16560 and 16575 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 16560 and 16575. First we will calculate the prime factors of 16560 and 16575.

Prime Factorization of 16560

Prime Factorization of 16575

Now multiplying the highest exponent prime factors to calculate the LCM of 16560 and 16575.

LCM(16560,16575) = 2⁴ × 3² × 5² × 23¹ × 13¹ × 17¹
LCM(16560,16575) = 18298800