Least Common Multiple of 360 and 366

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 366 the smallest integer that is 21960 that is divisible by both numbers.

Least Common Multiple (LCM) of 360 and 366 is 21960.

LCM(360,366) = 21960

LCM of 360 and 366

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

LCM of:
and

Least Common Multiple of 360 and 366

LCM of 360 and 366 is 21960

Least common multiple can be found by multiplying the highest exponent prime factors of 360 and 366. First we will calculate the prime factors of 360 and 366.

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 366


2 366
3 183
61 61
1

Prime factors of 366 are 2, 3,61. Prime factorization of 366 in exponential form is:

366 = 21×31×611

Now multiplying the highest exponent prime factors to calculate the LCM of 360 and 366.

LCM(360,366) = 23×32×51×611
LCM(360,366) = 21960

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 366

List of positive integer factors of 366 that divides 366 without a remainder.

1, 2, 3, 6, 61, 122, 183, 366

Least Common Multiple of 360 and 366 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 366, than apply into the LCM equation.

GCF(360,366) = 6
LCM(360,366) = ( 360 × 366) / 6
LCM(360,366) = 131760 / 6
LCM(360,366) = 21960

Properties of LCM 360 and 366

(i) The LCM of 366 and 360 is associative

LCM of 360 and 366 = LCM of 366 and 360

Related Least Common Multiples of 360

Related Least Common Multiples of 366

Frequently Asked Questions on LCM of 360 and 366

1. What is the LCM of 360 and 366?

Answer: LCM of 360 and 366 is 21960.

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 366?

Answer: Factors of 366 are 1, 2, 3, 6, 61, 122, 183, 366. There are 8 integers that are factors of 366. The greatest factor of 366 is 366.

4. How to Find the LCM of 360 and 366?

Answer:

Least Common Multiple of 360 and 366 = 21960

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 366

366 = 2 x 3 x 61

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

LCM = 21960 = 2 x 2 x 2 x 3 x 3 x 5 x 61

Step 4: Therefore, the least common multiple of 360 and 366 is 21960.