What is the Least Common Multiple of 1582 and 1592?

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 1582 and 1592 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1582 and 1592, than apply into the LCM equation.

GCF(1582,1592) = 2
LCM(1582,1592) = ( 1582 × 1592) / 2
LCM(1582,1592) = 2518544 / 2
LCM(1582,1592) = 1259272

Least Common Multiple (LCM) of 1582 and 1592 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1582 and 1592. First we will calculate the prime factors of 1582 and 1592.

Prime Factorization of 1582

Prime Factorization of 1592

Now multiplying the highest exponent prime factors to calculate the LCM of 1582 and 1592.

LCM(1582,1592) = 2³ × 7¹ × 113¹ × 199¹
LCM(1582,1592) = 1259272