Given Numbers are 410, 414

We can find the LCM of 410, 414 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 410 and 414

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

Multiples of 414 =414,828,1242,1656,2070,2484,2898,3312,3726,4140,4554,4968,5382,5796,6210,6624,7038,

Now, get the least common multiple of 410, 414 which is 84870

So, the LCM of 410, 414 is 84870.

One method for determining the LCM of 410 and 414 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 410's prime factorization:

Prime factors of 410 are 2, 5,41.

410 = 2¹×5¹×41¹

And this is 414's prime factorization:

Prime factors of 414 are 2, 3,23.

414 = 2¹×3²×23¹

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, 5,41, 3,23

2¹×3²×5¹×23¹×41¹ = 84870

This shows that the LCM of 410 and 414 is 84870.

The first step in determining the Least Common Multiple of 410 and 414 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 410 and 414:

Lets look at the first ten multiples of these numbers, 410 and 414:

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

414,828,1242,1656,2070,2484,2898,3312,3726,7038 are the first ten multiples of 414.

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 410 and 414, for example, are 4920, 6970, and 6624. 84870 is the least common multiple since it is the smallest.

410 and 414 have an LCM of 84870.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 410 and 414, than apply into the LCM equation.

GCF(410,414) = 2
LCM(410,414) = ( 410 × 414) / 2
LCM(410,414) = 169740 / 2
LCM(410,414) = 84870

1. What is the LCM of 410 and 414?

The LCM of 410 and 414 is 84870.

2. How to find the lowest common multiple of 410 and 414?

To find the lowest common multiple of 410 and 414, we have to get the multip;es of both numbers and identify the least common multiple in them which is 84870.

3. 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.

4. What are the Factors of 414?

Answer: Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414. There are 12 integers that are factors of 414. The greatest factor of 414 is 414.

Answer:

Least Common Multiple of 410 and 414 = 84870

Step 1: Find the prime factorization of 410

410 = 2 x 5 x 41

Step 2: Find the prime factorization of 414

414 = 2 x 3 x 3 x 23

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

LCM = 84870 = 2 x 3 x 3 x 5 x 23 x 41

Step 4: Therefore, the least common multiple of 410 and 414 is 84870.