What is the Least Common Multiple of 1567 and 1582?

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 1567 and 1582 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1567 and 1582, than apply into the LCM equation.

GCF(1567,1582) = 1
LCM(1567,1582) = ( 1567 × 1582) / 1
LCM(1567,1582) = 2478994 / 1
LCM(1567,1582) = 2478994

Least Common Multiple (LCM) of 1567 and 1582 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1567 and 1582. First we will calculate the prime factors of 1567 and 1582.

Prime Factorization of 1567

Prime Factorization of 1582

Now multiplying the highest exponent prime factors to calculate the LCM of 1567 and 1582.

LCM(1567,1582) = 1567¹ × 2¹ × 7¹ × 113¹
LCM(1567,1582) = 2478994