What is the Least Common Multiple of 1644 and 1664?

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 1644 and 1664 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1644 and 1664, than apply into the LCM equation.

GCF(1644,1664) = 4
LCM(1644,1664) = ( 1644 × 1664) / 4
LCM(1644,1664) = 2735616 / 4
LCM(1644,1664) = 683904

Least Common Multiple (LCM) of 1644 and 1664 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1644 and 1664. First we will calculate the prime factors of 1644 and 1664.

Prime Factorization of 1644

Prime Factorization of 1664

Now multiplying the highest exponent prime factors to calculate the LCM of 1644 and 1664.

LCM(1644,1664) = 2⁷ × 3¹ × 137¹ × 13¹
LCM(1644,1664) = 683904