What is the Least Common Multiple of 5760 and 5766?

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 5766 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 5766, than apply into the LCM equation.

GCF(5760,5766) = 6
LCM(5760,5766) = ( 5760 × 5766) / 6
LCM(5760,5766) = 33212160 / 6
LCM(5760,5766) = 5535360

Least Common Multiple (LCM) of 5760 and 5766 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5760 and 5766. First we will calculate the prime factors of 5760 and 5766.

Prime Factorization of 5760

Prime Factorization of 5766

Now multiplying the highest exponent prime factors to calculate the LCM of 5760 and 5766.

LCM(5760,5766) = 2⁷ × 3² × 5¹ × 31²
LCM(5760,5766) = 5535360