What is the Least Common Multiple of 21924 and 21936?

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 21924 and 21936 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21924 and 21936, than apply into the LCM equation.

GCF(21924,21936) = 12
LCM(21924,21936) = ( 21924 × 21936) / 12
LCM(21924,21936) = 480924864 / 12
LCM(21924,21936) = 40077072

Least Common Multiple (LCM) of 21924 and 21936 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21924 and 21936. First we will calculate the prime factors of 21924 and 21936.

Prime Factorization of 21924

Prime Factorization of 21936

Now multiplying the highest exponent prime factors to calculate the LCM of 21924 and 21936.

LCM(21924,21936) = 2⁴ × 3³ × 7¹ × 29¹ × 457¹
LCM(21924,21936) = 40077072