What is the Least Common Multiple of 5742 and 5762?

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 5762 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 5762, than apply into the LCM equation.

GCF(5742,5762) = 2
LCM(5742,5762) = ( 5742 × 5762) / 2
LCM(5742,5762) = 33085404 / 2
LCM(5742,5762) = 16542702

Least Common Multiple (LCM) of 5742 and 5762 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5742 and 5762. First we will calculate the prime factors of 5742 and 5762.

Prime Factorization of 5742

Prime Factorization of 5762

Now multiplying the highest exponent prime factors to calculate the LCM of 5742 and 5762.

LCM(5742,5762) = 2¹ × 3² × 11¹ × 29¹ × 43¹ × 67¹
LCM(5742,5762) = 16542702