What is the Least Common Multiple of 345 and 365?

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 365 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 365, than apply into the LCM equation.

GCF(345,365) = 5
LCM(345,365) = ( 345 × 365) / 5
LCM(345,365) = 125925 / 5
LCM(345,365) = 25185

Least Common Multiple (LCM) of 345 and 365 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 345 and 365. First we will calculate the prime factors of 345 and 365.

Prime Factorization of 345

Prime Factorization of 365

Now multiplying the highest exponent prime factors to calculate the LCM of 345 and 365.

LCM(345,365) = 3¹ × 5¹ × 23¹ × 73¹
LCM(345,365) = 25185