Least Common Multiple of 1400 and 1406

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 1406 the smallest integer that is 984200 that is divisible by both numbers.

Least Common Multiple (LCM) of 1400 and 1406 is 984200.

LCM(1400,1406) = 984200

LCM of 1400 and 1406

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

LCM of:
and

Least Common Multiple of 1400 and 1406

LCM of 1400 and 1406 is 984200

Least common multiple can be found by multiplying the highest exponent prime factors of 1400 and 1406. First we will calculate the prime factors of 1400 and 1406.

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 1406


2 1406
19 703
37 37
1

Prime factors of 1406 are 2, 19,37. Prime factorization of 1406 in exponential form is:

1406 = 21×191×371

Now multiplying the highest exponent prime factors to calculate the LCM of 1400 and 1406.

LCM(1400,1406) = 23×52×71×191×371
LCM(1400,1406) = 984200

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 1406

List of positive integer factors of 1406 that divides 1406 without a remainder.

1, 2, 19, 37, 38, 74, 703, 1406

Least Common Multiple of 1400 and 1406 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 1406, than apply into the LCM equation.

GCF(1400,1406) = 2
LCM(1400,1406) = ( 1400 × 1406) / 2
LCM(1400,1406) = 1968400 / 2
LCM(1400,1406) = 984200

Properties of LCM 1400 and 1406

(i) The LCM of 1406 and 1400 is associative

LCM of 1400 and 1406 = LCM of 1406 and 1400

Related Least Common Multiples of 1400

Related Least Common Multiples of 1406

Frequently Asked Questions on LCM of 1400 and 1406

1. What is the LCM of 1400 and 1406?

Answer: LCM of 1400 and 1406 is 984200.

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 1406?

Answer: Factors of 1406 are 1, 2, 19, 37, 38, 74, 703, 1406. There are 8 integers that are factors of 1406. The greatest factor of 1406 is 1406.

4. How to Find the LCM of 1400 and 1406?

Answer:

Least Common Multiple of 1400 and 1406 = 984200

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 1406

1406 = 2 x 19 x 37

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

LCM = 984200 = 2 x 2 x 2 x 5 x 5 x 7 x 19 x 37

Step 4: Therefore, the least common multiple of 1400 and 1406 is 984200.