What is the Least Common Multiple of 10405 and 10416?

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 10405 and 10416 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10405 and 10416, than apply into the LCM equation.

GCF(10405,10416) = 1
LCM(10405,10416) = ( 10405 × 10416) / 1
LCM(10405,10416) = 108378480 / 1
LCM(10405,10416) = 108378480

Least Common Multiple (LCM) of 10405 and 10416 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10405 and 10416. First we will calculate the prime factors of 10405 and 10416.

Prime Factorization of 10405

Prime Factorization of 10416

Now multiplying the highest exponent prime factors to calculate the LCM of 10405 and 10416.

LCM(10405,10416) = 5¹ × 2081¹ × 2⁴ × 3¹ × 7¹ × 31¹
LCM(10405,10416) = 108378480