What is the Least Common Multiple of 2742 and 2760?

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 2742 and 2760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2742 and 2760, than apply into the LCM equation.

GCF(2742,2760) = 6
LCM(2742,2760) = ( 2742 × 2760) / 6
LCM(2742,2760) = 7567920 / 6
LCM(2742,2760) = 1261320

Least Common Multiple (LCM) of 2742 and 2760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2742 and 2760. First we will calculate the prime factors of 2742 and 2760.

Prime Factorization of 2742

Prime Factorization of 2760

Now multiplying the highest exponent prime factors to calculate the LCM of 2742 and 2760.

LCM(2742,2760) = 2³ × 3¹ × 457¹ × 5¹ × 23¹
LCM(2742,2760) = 1261320