Given Numbers are 415, 421

We can find the LCM of 415, 421 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 415 and 421

Multiples of 415 =415,830,1245,1660,2075,2490,2905,3320,3735,4150,4565,4980,5395,5810,6225,6640,7055,

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 415, 421 which is 174715

So, the LCM of 415, 421 is 174715.

One method for determining the LCM of 415 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 415's prime factorization:

Prime factors of 415 are 5,83.

415 = 5¹×83¹

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: 5,83,421

5¹×83¹×421¹ = 174715

This shows that the LCM of 415 and 421 is 174715.

The first step in determining the Least Common Multiple of 415 and 421 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 415 and 421:

Lets look at the first ten multiples of these numbers, 415 and 421:

415,830,1245,1660,2075,2490,2905,3320,3735,7055 are the first ten multiples of 415.

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 415 and 421, for example, are 4980, 7055, and 6736. 174715 is the least common multiple since it is the smallest.

415 and 421 have an LCM of 174715.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 415 and 421, than apply into the LCM equation.

GCF(415,421) = 1
LCM(415,421) = ( 415 × 421) / 1
LCM(415,421) = 174715 / 1
LCM(415,421) = 174715

1. What is the LCM of 415 and 421?

The LCM of 415 and 421 is 174715.

2. How to find the lowest common multiple of 415 and 421?

To find the lowest common multiple of 415 and 421, we have to get the multip;es of both numbers and identify the least common multiple in them which is 174715.

3. What are the Factors of 415?

Answer: Factors of 415 are 1, 5, 83, 415. There are 4 integers that are factors of 415. The greatest factor of 415 is 415.

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 415 and 421 = 174715

Step 1: Find the prime factorization of 415

415 = 5 x 83

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 = 174715 = 5 x 83 x 421

Step 4: Therefore, the least common multiple of 415 and 421 is 174715.