What is the Least Common Multiple of 5760 and 5775?

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 5760 and 5775 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5760 and 5775, than apply into the LCM equation.

GCF(5760,5775) = 15
LCM(5760,5775) = ( 5760 × 5775) / 15
LCM(5760,5775) = 33264000 / 15
LCM(5760,5775) = 2217600

Least Common Multiple (LCM) of 5760 and 5775 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5760 and 5775. First we will calculate the prime factors of 5760 and 5775.

Prime Factorization of 5760

Prime Factorization of 5775

Now multiplying the highest exponent prime factors to calculate the LCM of 5760 and 5775.

LCM(5760,5775) = 2⁷ × 3² × 5² × 7¹ × 11¹
LCM(5760,5775) = 2217600