What is the Least Common Multiple of 21964 and 21984?

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 21964 and 21984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21964 and 21984, than apply into the LCM equation.

GCF(21964,21984) = 4
LCM(21964,21984) = ( 21964 × 21984) / 4
LCM(21964,21984) = 482856576 / 4
LCM(21964,21984) = 120714144

Least Common Multiple (LCM) of 21964 and 21984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21964 and 21984. First we will calculate the prime factors of 21964 and 21984.

Prime Factorization of 21964

Prime Factorization of 21984

Now multiplying the highest exponent prime factors to calculate the LCM of 21964 and 21984.

LCM(21964,21984) = 2⁵ × 17² × 19¹ × 3¹ × 229¹
LCM(21964,21984) = 120714144