What is the Least Common Multiple of 21744 and 21763?

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 21744 and 21763 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21744 and 21763, than apply into the LCM equation.

GCF(21744,21763) = 1
LCM(21744,21763) = ( 21744 × 21763) / 1
LCM(21744,21763) = 473214672 / 1
LCM(21744,21763) = 473214672

Least Common Multiple (LCM) of 21744 and 21763 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21744 and 21763. First we will calculate the prime factors of 21744 and 21763.

Prime Factorization of 21744

Prime Factorization of 21763

Now multiplying the highest exponent prime factors to calculate the LCM of 21744 and 21763.

LCM(21744,21763) = 2⁴ × 3² × 151¹ × 7¹ × 3109¹
LCM(21744,21763) = 473214672