What is the Least Common Multiple of 5742 and 5760?

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 5742 and 5760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5742 and 5760, than apply into the LCM equation.

GCF(5742,5760) = 18
LCM(5742,5760) = ( 5742 × 5760) / 18
LCM(5742,5760) = 33073920 / 18
LCM(5742,5760) = 1837440

Least Common Multiple (LCM) of 5742 and 5760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5742 and 5760. First we will calculate the prime factors of 5742 and 5760.

Prime Factorization of 5742

Prime Factorization of 5760

Now multiplying the highest exponent prime factors to calculate the LCM of 5742 and 5760.

LCM(5742,5760) = 2⁷ × 3² × 11¹ × 29¹ × 5¹
LCM(5742,5760) = 1837440