Least Common Multiple of 15360 and 15365

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 15360 and 15365 the smallest integer that is 47201280 that is divisible by both numbers.

Least Common Multiple (LCM) of 15360 and 15365 is 47201280.

LCM(15360,15365) = 47201280

LCM of 15360 and 15365

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

LCM of:
and

Least Common Multiple of 15360 and 15365

LCM of 15360 and 15365 is 47201280

Least common multiple can be found by multiplying the highest exponent prime factors of 15360 and 15365. First we will calculate the prime factors of 15360 and 15365.

Prime Factorization of 15360


2 15360
2 7680
2 3840
2 1920
2 960
2 480
2 240
2 120
2 60
2 30
3 15
5 5
1

Prime factors of 15360 are 2, 3,5. Prime factorization of 15360 in exponential form is:

15360 = 210×31×51

Prime Factorization of 15365


5 15365
7 3073
439 439
1

Prime factors of 15365 are 5, 7,439. Prime factorization of 15365 in exponential form is:

15365 = 51×71×4391

Now multiplying the highest exponent prime factors to calculate the LCM of 15360 and 15365.

LCM(15360,15365) = 210×31×51×71×4391
LCM(15360,15365) = 47201280

Factors of 15360

List of positive integer factors of 15360 that divides 15360 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1024, 1280, 1536, 1920, 2560, 3072, 3840, 5120, 7680, 15360

Factors of 15365

List of positive integer factors of 15365 that divides 15365 without a remainder.

1, 5, 7, 35, 439, 2195, 3073, 15365

Least Common Multiple of 15360 and 15365 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15360 and 15365, than apply into the LCM equation.

GCF(15360,15365) = 5
LCM(15360,15365) = ( 15360 × 15365) / 5
LCM(15360,15365) = 236006400 / 5
LCM(15360,15365) = 47201280

Properties of LCM 15360 and 15365

(i) The LCM of 15365 and 15360 is associative

LCM of 15360 and 15365 = LCM of 15365 and 15360

Related Least Common Multiples of 15360

Related Least Common Multiples of 15365

Frequently Asked Questions on LCM of 15360 and 15365

1. What is the LCM of 15360 and 15365?

Answer: LCM of 15360 and 15365 is 47201280.

2. What are the Factors of 15360?

Answer: Factors of 15360 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1024, 1280, 1536, 1920, 2560, 3072, 3840, 5120, 7680, 15360. There are 44 integers that are factors of 15360. The greatest factor of 15360 is 15360.

3. What are the Factors of 15365?

Answer: Factors of 15365 are 1, 5, 7, 35, 439, 2195, 3073, 15365. There are 8 integers that are factors of 15365. The greatest factor of 15365 is 15365.

4. How to Find the LCM of 15360 and 15365?

Answer:

Least Common Multiple of 15360 and 15365 = 47201280

Step 1: Find the prime factorization of 15360

15360 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 15365

15365 = 5 x 7 x 439

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

LCM = 47201280 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 439

Step 4: Therefore, the least common multiple of 15360 and 15365 is 47201280.