What is the Least Common Multiple of 1138 and 1148?

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 1138 and 1148 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1138 and 1148, than apply into the LCM equation.

GCF(1138,1148) = 2
LCM(1138,1148) = ( 1138 × 1148) / 2
LCM(1138,1148) = 1306424 / 2
LCM(1138,1148) = 653212

Least Common Multiple (LCM) of 1138 and 1148 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1138 and 1148. First we will calculate the prime factors of 1138 and 1148.

Prime Factorization of 1138

Prime Factorization of 1148

Now multiplying the highest exponent prime factors to calculate the LCM of 1138 and 1148.

LCM(1138,1148) = 2² × 569¹ × 7¹ × 41¹
LCM(1138,1148) = 653212