What is the Least Common Multiple of 345 and 349?

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 345 and 349 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 345 and 349, than apply into the LCM equation.

GCF(345,349) = 1
LCM(345,349) = ( 345 × 349) / 1
LCM(345,349) = 120405 / 1
LCM(345,349) = 120405

Least Common Multiple (LCM) of 345 and 349 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 345 and 349. First we will calculate the prime factors of 345 and 349.

Prime Factorization of 345

Prime Factorization of 349

Now multiplying the highest exponent prime factors to calculate the LCM of 345 and 349.

LCM(345,349) = 3¹ × 5¹ × 23¹ × 349¹
LCM(345,349) = 120405