Least Common Multiple of 364 and 365

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 364 and 365 the smallest integer that is 132860 that is divisible by both numbers.

Least Common Multiple (LCM) of 364 and 365 is 132860.

LCM(364,365) = 132860

LCM of 364 and 365

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 364 and 365

LCM of 364 and 365 is 132860

Least common multiple can be found by multiplying the highest exponent prime factors of 364 and 365. First we will calculate the prime factors of 364 and 365.

Prime Factorization of 364


2 364
2 182
7 91
13 13
1

Prime factors of 364 are 2, 7,13. Prime factorization of 364 in exponential form is:

364 = 22×71×131

Prime Factorization of 365


5 365
73 73
1

Prime factors of 365 are 5,73. Prime factorization of 365 in exponential form is:

365 = 51×731

Now multiplying the highest exponent prime factors to calculate the LCM of 364 and 365.

LCM(364,365) = 22×51×71×131×731
LCM(364,365) = 132860

Factors of 364

List of positive integer factors of 364 that divides 364 without a remainder.

1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364

Factors of 365

List of positive integer factors of 365 that divides 365 without a remainder.

1, 5, 73, 365

Least Common Multiple of 364 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 364 and 365, than apply into the LCM equation.

GCF(364,365) = 1
LCM(364,365) = ( 364 × 365) / 1
LCM(364,365) = 132860 / 1
LCM(364,365) = 132860

Properties of LCM 364 and 365

(i) The LCM of 365 and 364 is associative

LCM of 364 and 365 = LCM of 365 and 364

Related Least Common Multiples of 364

Related Least Common Multiples of 365

Frequently Asked Questions on LCM of 364 and 365

1. What is the LCM of 364 and 365?

Answer: LCM of 364 and 365 is 132860.

2. What are the Factors of 364?

Answer: Factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364. There are 12 integers that are factors of 364. The greatest factor of 364 is 364.

3. What are the Factors of 365?

Answer: Factors of 365 are 1, 5, 73, 365. There are 4 integers that are factors of 365. The greatest factor of 365 is 365.

4. How to Find the LCM of 364 and 365?

Answer:

Least Common Multiple of 364 and 365 = 132860

Step 1: Find the prime factorization of 364

364 = 2 x 2 x 7 x 13

Step 2: Find the prime factorization of 365

365 = 5 x 73

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 132860 = 2 x 2 x 5 x 7 x 13 x 73

Step 4: Therefore, the least common multiple of 364 and 365 is 132860.