What is the Least Common Multiple of 1582 and 1602?

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 1602 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 1602, than apply into the LCM equation.

GCF(1582,1602) = 2
LCM(1582,1602) = ( 1582 × 1602) / 2
LCM(1582,1602) = 2534364 / 2
LCM(1582,1602) = 1267182

Least Common Multiple (LCM) of 1582 and 1602 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1582 and 1602. First we will calculate the prime factors of 1582 and 1602.

Prime Factorization of 1582

Prime Factorization of 1602

Now multiplying the highest exponent prime factors to calculate the LCM of 1582 and 1602.

LCM(1582,1602) = 2¹ × 7¹ × 113¹ × 3² × 89¹
LCM(1582,1602) = 1267182