Given Numbers are 416, 421

We can find the LCM of 416, 421 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 416 and 421

Multiples of 416 =416,832,1248,1664,2080,2496,2912,3328,3744,4160,4576,4992,5408,5824,6240,6656,7072,

Multiples of 421 =421,842,1263,1684,2105,2526,2947,3368,3789,4210,4631,5052,5473,5894,6315,6736,7157,

Now, get the least common multiple of 416, 421 which is 175136

So, the LCM of 416, 421 is 175136.

One method for determining the LCM of 416 and 421 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 416's prime factorization:

Prime factors of 416 are 2,13.

416 = 2⁵×13¹

And this is 421's prime factorization:

Prime factors of 421 are 421.

421 = 421¹

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: 2,13,421

2⁵×13¹×421¹ = 175136

This shows that the LCM of 416 and 421 is 175136.

The first step in determining the Least Common Multiple of 416 and 421 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 416 and 421:

Lets look at the first ten multiples of these numbers, 416 and 421:

416,832,1248,1664,2080,2496,2912,3328,3744,7072 are the first ten multiples of 416.

421,842,1263,1684,2105,2526,2947,3368,3789,7157 are the first ten multiples of 421.

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 416 and 421, for example, are 4992, 7072, and 6736. 175136 is the least common multiple since it is the smallest.

416 and 421 have an LCM of 175136.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 416 and 421, than apply into the LCM equation.

GCF(416,421) = 1
LCM(416,421) = ( 416 × 421) / 1
LCM(416,421) = 175136 / 1
LCM(416,421) = 175136

1. What is the LCM of 416 and 421?

The LCM of 416 and 421 is 175136.

2. How to find the lowest common multiple of 416 and 421?

To find the lowest common multiple of 416 and 421, we have to get the multip;es of both numbers and identify the least common multiple in them which is 175136.

3. What are the Factors of 416?

Answer: Factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416. There are 12 integers that are factors of 416. The greatest factor of 416 is 416.

4. What are the Factors of 421?

Answer: Factors of 421 are 1, 421. There are 2 integers that are factors of 421. The greatest factor of 421 is 421.

Answer:

Least Common Multiple of 416 and 421 = 175136

Step 1: Find the prime factorization of 416

416 = 2 x 2 x 2 x 2 x 2 x 13

Step 2: Find the prime factorization of 421

421 = 421

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

LCM = 175136 = 2 x 2 x 2 x 2 x 2 x 13 x 421

Step 4: Therefore, the least common multiple of 416 and 421 is 175136.