What is the Least Common Multiple of 21200 and 21212?

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 21200 and 21212 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21200 and 21212, than apply into the LCM equation.

GCF(21200,21212) = 4
LCM(21200,21212) = ( 21200 × 21212) / 4
LCM(21200,21212) = 449694400 / 4
LCM(21200,21212) = 112423600

Least Common Multiple (LCM) of 21200 and 21212 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21200 and 21212. First we will calculate the prime factors of 21200 and 21212.

Prime Factorization of 21200

Prime Factorization of 21212

Now multiplying the highest exponent prime factors to calculate the LCM of 21200 and 21212.

LCM(21200,21212) = 2⁴ × 5² × 53¹ × 5303¹
LCM(21200,21212) = 112423600