Given Numbers are 406, 410

We can find the LCM of 406, 410 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 406 and 410

Multiples of 406 =406,812,1218,1624,2030,2436,2842,3248,3654,4060,4466,4872,5278,5684,6090,6496,6902,

Multiples of 410 =410,820,1230,1640,2050,2460,2870,3280,3690,4100,4510,4920,5330,5740,6150,6560,6970,

Now, get the least common multiple of 406, 410 which is 83230

So, the LCM of 406, 410 is 83230.

One method for determining the LCM of 406 and 410 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:

Here is 406's prime factorization:

Prime factors of 406 are 2, 7,29.

406 = 2¹×7¹×29¹

And this is 410's prime factorization:

Prime factors of 410 are 2, 5,41.

410 = 2¹×5¹×41¹

When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 2, 7,29, 5,41

2¹×5¹×7¹×29¹×41¹ = 83230

This shows that the LCM of 406 and 410 is 83230.

The first step in determining the Least Common Multiple of 406 and 410 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 406 and 410:

Lets look at the first ten multiples of these numbers, 406 and 410:

406,812,1218,1624,2030,2436,2842,3248,3654,6902 are the first ten multiples of 406.

410,820,1230,1640,2050,2460,2870,3280,3690,6970 are the first ten multiples of 410.

You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 406 and 410, for example, are 4872, 6902, and 6560. 83230 is the least common multiple since it is the smallest.

406 and 410 have an LCM of 83230.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 406 and 410, than apply into the LCM equation.

GCF(406,410) = 2
LCM(406,410) = ( 406 × 410) / 2
LCM(406,410) = 166460 / 2
LCM(406,410) = 83230

1. What is the LCM of 406 and 410?

The LCM of 406 and 410 is 83230.

2. How to find the lowest common multiple of 406 and 410?

To find the lowest common multiple of 406 and 410, we have to get the multip;es of both numbers and identify the least common multiple in them which is 83230.

3. What are the Factors of 406?

Answer: Factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406. There are 8 integers that are factors of 406. The greatest factor of 406 is 406.

4. What are the Factors of 410?

Answer: Factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410. There are 8 integers that are factors of 410. The greatest factor of 410 is 410.

Answer:

Least Common Multiple of 406 and 410 = 83230

Step 1: Find the prime factorization of 406

406 = 2 x 7 x 29

Step 2: Find the prime factorization of 410

410 = 2 x 5 x 41

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

LCM = 83230 = 2 x 5 x 7 x 29 x 41

Step 4: Therefore, the least common multiple of 406 and 410 is 83230.