What is the Least Common Multiple of 21744 and 21752?

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 21752 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 21752, than apply into the LCM equation.

GCF(21744,21752) = 8
LCM(21744,21752) = ( 21744 × 21752) / 8
LCM(21744,21752) = 472975488 / 8
LCM(21744,21752) = 59121936

Least Common Multiple (LCM) of 21744 and 21752 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21744 and 21752. First we will calculate the prime factors of 21744 and 21752.

Prime Factorization of 21744

Prime Factorization of 21752

Now multiplying the highest exponent prime factors to calculate the LCM of 21744 and 21752.

LCM(21744,21752) = 2⁴ × 3² × 151¹ × 2719¹
LCM(21744,21752) = 59121936