What is the Least Common Multiple of 365 and 380?

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 365 and 380 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 365 and 380, than apply into the LCM equation.

GCF(365,380) = 5
LCM(365,380) = ( 365 × 380) / 5
LCM(365,380) = 138700 / 5
LCM(365,380) = 27740

Least Common Multiple (LCM) of 365 and 380 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 365 and 380. First we will calculate the prime factors of 365 and 380.

Prime Factorization of 365

Prime Factorization of 380

Now multiplying the highest exponent prime factors to calculate the LCM of 365 and 380.

LCM(365,380) = 5¹ × 73¹ × 2² × 19¹
LCM(365,380) = 27740