What is the Least Common Multiple of 3400 and 3405?

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 3400 and 3405 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3400 and 3405, than apply into the LCM equation.

GCF(3400,3405) = 5
LCM(3400,3405) = ( 3400 × 3405) / 5
LCM(3400,3405) = 11577000 / 5
LCM(3400,3405) = 2315400

Least Common Multiple (LCM) of 3400 and 3405 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3400 and 3405. First we will calculate the prime factors of 3400 and 3405.

Prime Factorization of 3400

Prime Factorization of 3405

Now multiplying the highest exponent prime factors to calculate the LCM of 3400 and 3405.

LCM(3400,3405) = 2³ × 5² × 17¹ × 3¹ × 227¹
LCM(3400,3405) = 2315400