Least Common Multiple of 360 and 361

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 361 the smallest integer that is 129960 that is divisible by both numbers.

Least Common Multiple (LCM) of 360 and 361 is 129960.

LCM(360,361) = 129960

LCM of 360 and 361

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

LCM of:
and

Least Common Multiple of 360 and 361

LCM of 360 and 361 is 129960

Least common multiple can be found by multiplying the highest exponent prime factors of 360 and 361. First we will calculate the prime factors of 360 and 361.

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 361


19 361
19 19
1

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

361 = 192

Now multiplying the highest exponent prime factors to calculate the LCM of 360 and 361.

LCM(360,361) = 23×32×51×192
LCM(360,361) = 129960

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 361

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

1, 19, 361

Least Common Multiple of 360 and 361 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 361, than apply into the LCM equation.

GCF(360,361) = 1
LCM(360,361) = ( 360 × 361) / 1
LCM(360,361) = 129960 / 1
LCM(360,361) = 129960

Properties of LCM 360 and 361

(i) The LCM of 361 and 360 is associative

LCM of 360 and 361 = LCM of 361 and 360

Related Least Common Multiples of 360

Related Least Common Multiples of 361

Frequently Asked Questions on LCM of 360 and 361

1. What is the LCM of 360 and 361?

Answer: LCM of 360 and 361 is 129960.

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 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.

4. How to Find the LCM of 360 and 361?

Answer:

Least Common Multiple of 360 and 361 = 129960

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 361

361 = 19 x 19

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

LCM = 129960 = 2 x 2 x 2 x 3 x 3 x 5 x 19 x 19

Step 4: Therefore, the least common multiple of 360 and 361 is 129960.