Least Common Multiple of 360 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 360 and 364 the smallest integer that is 32760 that is divisible by both numbers.

Least Common Multiple (LCM) of 360 and 364 is 32760.

LCM(360,364) = 32760

LCM of 360 and 364

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

LCM of:
and

Least Common Multiple of 360 and 364

LCM of 360 and 364 is 32760

Least common multiple can be found by multiplying the highest exponent prime factors of 360 and 364. First we will calculate the prime factors of 360 and 364.

Prime Factorization of 360


2 360
2 180
2 90
3 45
3 15
5 5
1

Prime factors of 360 are 2, 3,5. Prime factorization of 360 in exponential form is:

360 = 23×32×51

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 360 and 364.

LCM(360,364) = 23×32×51×71×131
LCM(360,364) = 32760

Factors of 360

List of positive integer factors of 360 that divides 360 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

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 360 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 360 and 364, than apply into the LCM equation.

GCF(360,364) = 4
LCM(360,364) = ( 360 × 364) / 4
LCM(360,364) = 131040 / 4
LCM(360,364) = 32760

Properties of LCM 360 and 364

(i) The LCM of 364 and 360 is associative

LCM of 360 and 364 = LCM of 364 and 360

Related Least Common Multiples of 360

Related Least Common Multiples of 364

Frequently Asked Questions on LCM of 360 and 364

1. What is the LCM of 360 and 364?

Answer: LCM of 360 and 364 is 32760.

2. What are the Factors of 360?

Answer: Factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. There are 24 integers that are factors of 360. The greatest factor of 360 is 360.

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 360 and 364?

Answer:

Least Common Multiple of 360 and 364 = 32760

Step 1: Find the prime factorization of 360

360 = 2 x 2 x 2 x 3 x 3 x 5

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 = 32760 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 13

Step 4: Therefore, the least common multiple of 360 and 364 is 32760.