Least Common Multiple of 361 and 364

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 361 and 364 the smallest integer that is 131404 that is divisible by both numbers.

Least Common Multiple (LCM) of 361 and 364 is 131404.

LCM(361,364) = 131404

LCM of 361 and 364

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

LCM of:
and

Least Common Multiple of 361 and 364

LCM of 361 and 364 is 131404

Least common multiple can be found by multiplying the highest exponent prime factors of 361 and 364. First we will calculate the prime factors of 361 and 364.

Prime Factorization of 361


19 361
19 19
1

Prime factors of 361 are 19. Prime factorization of 361 in exponential form is:

361 = 192

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

Now multiplying the highest exponent prime factors to calculate the LCM of 361 and 364.

LCM(361,364) = 22×71×131×192
LCM(361,364) = 131404

Factors of 361

List of positive integer factors of 361 that divides 361 without a remainder.

1, 19, 361

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

Least Common Multiple of 361 and 364 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 361 and 364, than apply into the LCM equation.

GCF(361,364) = 1
LCM(361,364) = ( 361 × 364) / 1
LCM(361,364) = 131404 / 1
LCM(361,364) = 131404

Properties of LCM 361 and 364

(i) The LCM of 364 and 361 is associative

LCM of 361 and 364 = LCM of 364 and 361

Related Least Common Multiples of 361

Related Least Common Multiples of 364

Frequently Asked Questions on LCM of 361 and 364

1. What is the LCM of 361 and 364?

Answer: LCM of 361 and 364 is 131404.

2. What are the Factors of 361?

Answer: Factors of 361 are 1, 19, 361. There are 3 integers that are factors of 361. The greatest factor of 361 is 361.

3. 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.

4. How to Find the LCM of 361 and 364?

Answer:

Least Common Multiple of 361 and 364 = 131404

Step 1: Find the prime factorization of 361

361 = 19 x 19

Step 2: Find the prime factorization of 364

364 = 2 x 2 x 7 x 13

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

LCM = 131404 = 2 x 2 x 7 x 13 x 19 x 19

Step 4: Therefore, the least common multiple of 361 and 364 is 131404.