What is the Least Common Multiple of 10560 and 10575?

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 10560 and 10575 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10560 and 10575, than apply into the LCM equation.

GCF(10560,10575) = 15
LCM(10560,10575) = ( 10560 × 10575) / 15
LCM(10560,10575) = 111672000 / 15
LCM(10560,10575) = 7444800

Least Common Multiple (LCM) of 10560 and 10575 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10560 and 10575. First we will calculate the prime factors of 10560 and 10575.

Prime Factorization of 10560

Prime Factorization of 10575

Now multiplying the highest exponent prime factors to calculate the LCM of 10560 and 10575.

LCM(10560,10575) = 2⁶ × 3² × 5² × 11¹ × 47¹
LCM(10560,10575) = 7444800