What is the Least Common Multiple of 81405 and 81414?

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 81405 and 81414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 81405 and 81414, than apply into the LCM equation.

GCF(81405,81414) = 9
LCM(81405,81414) = ( 81405 × 81414) / 9
LCM(81405,81414) = 6627506670 / 9
LCM(81405,81414) = 736389630

Least Common Multiple (LCM) of 81405 and 81414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 81405 and 81414. First we will calculate the prime factors of 81405 and 81414.

Prime Factorization of 81405

Prime Factorization of 81414

Now multiplying the highest exponent prime factors to calculate the LCM of 81405 and 81414.

LCM(81405,81414) = 3⁵ × 5¹ × 67¹ × 2¹ × 4523¹
LCM(81405,81414) = 736389630