What is the Least Common Multiple of 21405 and 21414?

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 21405 and 21414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21405 and 21414, than apply into the LCM equation.

GCF(21405,21414) = 3
LCM(21405,21414) = ( 21405 × 21414) / 3
LCM(21405,21414) = 458366670 / 3
LCM(21405,21414) = 152788890

Least Common Multiple (LCM) of 21405 and 21414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21405 and 21414. First we will calculate the prime factors of 21405 and 21414.

Prime Factorization of 21405

Prime Factorization of 21414

Now multiplying the highest exponent prime factors to calculate the LCM of 21405 and 21414.

LCM(21405,21414) = 3¹ × 5¹ × 1427¹ × 2¹ × 43¹ × 83¹
LCM(21405,21414) = 152788890