Least Common Multiple of 1400 and 1405

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1400 and 1405 the smallest integer that is 393400 that is divisible by both numbers.

Least Common Multiple (LCM) of 1400 and 1405 is 393400.

LCM(1400,1405) = 393400

LCM of 1400 and 1405

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

LCM of:
and

Least Common Multiple of 1400 and 1405

LCM of 1400 and 1405 is 393400

Least common multiple can be found by multiplying the highest exponent prime factors of 1400 and 1405. First we will calculate the prime factors of 1400 and 1405.

Prime Factorization of 1400


2 1400
2 700
2 350
5 175
5 35
7 7
1

Prime factors of 1400 are 2, 5,7. Prime factorization of 1400 in exponential form is:

1400 = 23×52×71

Prime Factorization of 1405


5 1405
281 281
1

Prime factors of 1405 are 5,281. Prime factorization of 1405 in exponential form is:

1405 = 51×2811

Now multiplying the highest exponent prime factors to calculate the LCM of 1400 and 1405.

LCM(1400,1405) = 23×52×71×2811
LCM(1400,1405) = 393400

Factors of 1400

List of positive integer factors of 1400 that divides 1400 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400

Factors of 1405

List of positive integer factors of 1405 that divides 1405 without a remainder.

1, 5, 281, 1405

Least Common Multiple of 1400 and 1405 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1400 and 1405, than apply into the LCM equation.

GCF(1400,1405) = 5
LCM(1400,1405) = ( 1400 × 1405) / 5
LCM(1400,1405) = 1967000 / 5
LCM(1400,1405) = 393400

Properties of LCM 1400 and 1405

(i) The LCM of 1405 and 1400 is associative

LCM of 1400 and 1405 = LCM of 1405 and 1400

Related Least Common Multiples of 1400

Related Least Common Multiples of 1405

Frequently Asked Questions on LCM of 1400 and 1405

1. What is the LCM of 1400 and 1405?

Answer: LCM of 1400 and 1405 is 393400.

2. What are the Factors of 1400?

Answer: Factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400. There are 24 integers that are factors of 1400. The greatest factor of 1400 is 1400.

3. What are the Factors of 1405?

Answer: Factors of 1405 are 1, 5, 281, 1405. There are 4 integers that are factors of 1405. The greatest factor of 1405 is 1405.

4. How to Find the LCM of 1400 and 1405?

Answer:

Least Common Multiple of 1400 and 1405 = 393400

Step 1: Find the prime factorization of 1400

1400 = 2 x 2 x 2 x 5 x 5 x 7

Step 2: Find the prime factorization of 1405

1405 = 5 x 281

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

LCM = 393400 = 2 x 2 x 2 x 5 x 5 x 7 x 281

Step 4: Therefore, the least common multiple of 1400 and 1405 is 393400.