What is the Least Common Multiple of 21210 and 21225?

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 21210 and 21225 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21210 and 21225, than apply into the LCM equation.

GCF(21210,21225) = 15
LCM(21210,21225) = ( 21210 × 21225) / 15
LCM(21210,21225) = 450182250 / 15
LCM(21210,21225) = 30012150

Least Common Multiple (LCM) of 21210 and 21225 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21210 and 21225. First we will calculate the prime factors of 21210 and 21225.

Prime Factorization of 21210

Prime Factorization of 21225

Now multiplying the highest exponent prime factors to calculate the LCM of 21210 and 21225.

LCM(21210,21225) = 2¹ × 3¹ × 5² × 7¹ × 101¹ × 283¹
LCM(21210,21225) = 30012150