What is the Least Common Multiple of 1140 and 1154?

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 1140 and 1154 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1140 and 1154, than apply into the LCM equation.

GCF(1140,1154) = 2
LCM(1140,1154) = ( 1140 × 1154) / 2
LCM(1140,1154) = 1315560 / 2
LCM(1140,1154) = 657780

Least Common Multiple (LCM) of 1140 and 1154 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1140 and 1154. First we will calculate the prime factors of 1140 and 1154.

Prime Factorization of 1140

Prime Factorization of 1154

Now multiplying the highest exponent prime factors to calculate the LCM of 1140 and 1154.

LCM(1140,1154) = 2² × 3¹ × 5¹ × 19¹ × 577¹
LCM(1140,1154) = 657780