What is the Least Common Multiple of 1764 and 1782?

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 1764 and 1782 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1764 and 1782, than apply into the LCM equation.

GCF(1764,1782) = 18
LCM(1764,1782) = ( 1764 × 1782) / 18
LCM(1764,1782) = 3143448 / 18
LCM(1764,1782) = 174636

Least Common Multiple (LCM) of 1764 and 1782 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1764 and 1782. First we will calculate the prime factors of 1764 and 1782.

Prime Factorization of 1764

Prime Factorization of 1782

Now multiplying the highest exponent prime factors to calculate the LCM of 1764 and 1782.

LCM(1764,1782) = 2² × 3⁴ × 7² × 11¹
LCM(1764,1782) = 174636