Given Numbers are 402, 410

We can find the LCM of 402, 410 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 402 and 410

Multiples of 402 =402,804,1206,1608,2010,2412,2814,3216,3618,4020,4422,4824,5226,5628,6030,6432,6834,

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 402, 410 which is 82410

So, the LCM of 402, 410 is 82410.

One method for determining the LCM of 402 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 402's prime factorization:

Prime factors of 402 are 2, 3,67.

402 = 2¹×3¹×67¹

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, 3,67, 5,41

2¹×3¹×5¹×41¹×67¹ = 82410

This shows that the LCM of 402 and 410 is 82410.

The first step in determining the Least Common Multiple of 402 and 410 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 402 and 410:

Lets look at the first ten multiples of these numbers, 402 and 410:

402,804,1206,1608,2010,2412,2814,3216,3618,6834 are the first ten multiples of 402.

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 402 and 410, for example, are 4824, 6834, and 6560. 82410 is the least common multiple since it is the smallest.

402 and 410 have an LCM of 82410.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 402 and 410, than apply into the LCM equation.

GCF(402,410) = 2
LCM(402,410) = ( 402 × 410) / 2
LCM(402,410) = 164820 / 2
LCM(402,410) = 82410

1. What is the LCM of 402 and 410?

The LCM of 402 and 410 is 82410.

2. How to find the lowest common multiple of 402 and 410?

To find the lowest common multiple of 402 and 410, we have to get the multip;es of both numbers and identify the least common multiple in them which is 82410.

3. What are the Factors of 402?

Answer: Factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402. There are 8 integers that are factors of 402. The greatest factor of 402 is 402.

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 402 and 410 = 82410

Step 1: Find the prime factorization of 402

402 = 2 x 3 x 67

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 = 82410 = 2 x 3 x 5 x 41 x 67

Step 4: Therefore, the least common multiple of 402 and 410 is 82410.