Least Common Multiple of 1365 and 1370

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1365 and 1370 the smallest integer that is 374010 that is divisible by both numbers.

Least Common Multiple (LCM) of 1365 and 1370 is 374010.

LCM(1365,1370) = 374010

LCM of 1365 and 1370

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

LCM of:
and

Least Common Multiple of 1365 and 1370

LCM of 1365 and 1370 is 374010

Least common multiple can be found by multiplying the highest exponent prime factors of 1365 and 1370. First we will calculate the prime factors of 1365 and 1370.

Prime Factorization of 1365


3 1365
5 455
7 91
13 13
1

Prime factors of 1365 are 3, 5, 7,13. Prime factorization of 1365 in exponential form is:

1365 = 31×51×71×131

Prime Factorization of 1370


2 1370
5 685
137 137
1

Prime factors of 1370 are 2, 5,137. Prime factorization of 1370 in exponential form is:

1370 = 21×51×1371

Now multiplying the highest exponent prime factors to calculate the LCM of 1365 and 1370.

LCM(1365,1370) = 21×31×51×71×131×1371
LCM(1365,1370) = 374010

Factors of 1365

List of positive integer factors of 1365 that divides 1365 without a remainder.

1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365

Factors of 1370

List of positive integer factors of 1370 that divides 1370 without a remainder.

1, 2, 5, 10, 137, 274, 685, 1370

Least Common Multiple of 1365 and 1370 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1365 and 1370, than apply into the LCM equation.

GCF(1365,1370) = 5
LCM(1365,1370) = ( 1365 × 1370) / 5
LCM(1365,1370) = 1870050 / 5
LCM(1365,1370) = 374010

Properties of LCM 1365 and 1370

(i) The LCM of 1370 and 1365 is associative

LCM of 1365 and 1370 = LCM of 1370 and 1365

Related Least Common Multiples of 1365

Related Least Common Multiples of 1370

Frequently Asked Questions on LCM of 1365 and 1370

1. What is the LCM of 1365 and 1370?

Answer: LCM of 1365 and 1370 is 374010.

2. What are the Factors of 1365?

Answer: Factors of 1365 are 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365. There are 16 integers that are factors of 1365. The greatest factor of 1365 is 1365.

3. What are the Factors of 1370?

Answer: Factors of 1370 are 1, 2, 5, 10, 137, 274, 685, 1370. There are 8 integers that are factors of 1370. The greatest factor of 1370 is 1370.

4. How to Find the LCM of 1365 and 1370?

Answer:

Least Common Multiple of 1365 and 1370 = 374010

Step 1: Find the prime factorization of 1365

1365 = 3 x 5 x 7 x 13

Step 2: Find the prime factorization of 1370

1370 = 2 x 5 x 137

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

LCM = 374010 = 2 x 3 x 5 x 7 x 13 x 137

Step 4: Therefore, the least common multiple of 1365 and 1370 is 374010.