Least Common Multiple of 8400 and 8406

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 8400 and 8406 the smallest integer that is 11768400 that is divisible by both numbers.

Least Common Multiple (LCM) of 8400 and 8406 is 11768400.

LCM(8400,8406) = 11768400

LCM of 8400 and 8406

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

LCM of:
and

Least Common Multiple of 8400 and 8406

LCM of 8400 and 8406 is 11768400

Least common multiple can be found by multiplying the highest exponent prime factors of 8400 and 8406. First we will calculate the prime factors of 8400 and 8406.

Prime Factorization of 8400


2 8400
2 4200
2 2100
2 1050
3 525
5 175
5 35
7 7
1

Prime factors of 8400 are 2, 3, 5,7. Prime factorization of 8400 in exponential form is:

8400 = 24×31×52×71

Prime Factorization of 8406


2 8406
3 4203
3 1401
467 467
1

Prime factors of 8406 are 2, 3,467. Prime factorization of 8406 in exponential form is:

8406 = 21×32×4671

Now multiplying the highest exponent prime factors to calculate the LCM of 8400 and 8406.

LCM(8400,8406) = 24×32×52×71×4671
LCM(8400,8406) = 11768400

Factors of 8400

List of positive integer factors of 8400 that divides 8400 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 140, 150, 168, 175, 200, 210, 240, 280, 300, 336, 350, 400, 420, 525, 560, 600, 700, 840, 1050, 1200, 1400, 1680, 2100, 2800, 4200, 8400

Factors of 8406

List of positive integer factors of 8406 that divides 8406 without a remainder.

1, 2, 3, 6, 9, 18, 467, 934, 1401, 2802, 4203, 8406

Least Common Multiple of 8400 and 8406 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8400 and 8406, than apply into the LCM equation.

GCF(8400,8406) = 6
LCM(8400,8406) = ( 8400 × 8406) / 6
LCM(8400,8406) = 70610400 / 6
LCM(8400,8406) = 11768400

Properties of LCM 8400 and 8406

(i) The LCM of 8406 and 8400 is associative

LCM of 8400 and 8406 = LCM of 8406 and 8400

Related Least Common Multiples of 8400

Related Least Common Multiples of 8406

Frequently Asked Questions on LCM of 8400 and 8406

1. What is the LCM of 8400 and 8406?

Answer: LCM of 8400 and 8406 is 11768400.

2. What are the Factors of 8400?

Answer: Factors of 8400 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 140, 150, 168, 175, 200, 210, 240, 280, 300, 336, 350, 400, 420, 525, 560, 600, 700, 840, 1050, 1200, 1400, 1680, 2100, 2800, 4200, 8400. There are 60 integers that are factors of 8400. The greatest factor of 8400 is 8400.

3. What are the Factors of 8406?

Answer: Factors of 8406 are 1, 2, 3, 6, 9, 18, 467, 934, 1401, 2802, 4203, 8406. There are 12 integers that are factors of 8406. The greatest factor of 8406 is 8406.

4. How to Find the LCM of 8400 and 8406?

Answer:

Least Common Multiple of 8400 and 8406 = 11768400

Step 1: Find the prime factorization of 8400

8400 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7

Step 2: Find the prime factorization of 8406

8406 = 2 x 3 x 3 x 467

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

LCM = 11768400 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 7 x 467

Step 4: Therefore, the least common multiple of 8400 and 8406 is 11768400.