What is the Least Common Multiple of 3405 and 3423?

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 3405 and 3423 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3405 and 3423, than apply into the LCM equation.

GCF(3405,3423) = 3
LCM(3405,3423) = ( 3405 × 3423) / 3
LCM(3405,3423) = 11655315 / 3
LCM(3405,3423) = 3885105

Least Common Multiple (LCM) of 3405 and 3423 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3405 and 3423. First we will calculate the prime factors of 3405 and 3423.

Prime Factorization of 3405

Prime Factorization of 3423

Now multiplying the highest exponent prime factors to calculate the LCM of 3405 and 3423.

LCM(3405,3423) = 3¹ × 5¹ × 227¹ × 7¹ × 163¹
LCM(3405,3423) = 3885105