Given Numbers are 413, 420

We can find the LCM of 413, 420 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 413 and 420

Multiples of 413 =413,826,1239,1652,2065,2478,2891,3304,3717,4130,4543,4956,5369,5782,6195,6608,7021,

Multiples of 420 =420,840,1260,1680,2100,2520,2940,3360,3780,4200,4620,5040,5460,5880,6300,6720,7140,

Now, get the least common multiple of 413, 420 which is 24780

So, the LCM of 413, 420 is 24780.

One method for determining the LCM of 413 and 420 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 413's prime factorization:

Prime factors of 413 are 7,59.

413 = 7¹×59¹

And this is 420's prime factorization:

Prime factors of 420 are 2, 3, 5,7.

420 = 2²×3¹×5¹×7¹

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: 7,59, 2, 3,5

2²×3¹×5¹×7¹×59¹ = 24780

This shows that the LCM of 413 and 420 is 24780.

The first step in determining the Least Common Multiple of 413 and 420 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 413 and 420:

Lets look at the first ten multiples of these numbers, 413 and 420:

413,826,1239,1652,2065,2478,2891,3304,3717,7021 are the first ten multiples of 413.

420,840,1260,1680,2100,2520,2940,3360,3780,7140 are the first ten multiples of 420.

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 413 and 420, for example, are 4956, 7021, and 6720. 24780 is the least common multiple since it is the smallest.

413 and 420 have an LCM of 24780.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 413 and 420, than apply into the LCM equation.

GCF(413,420) = 7
LCM(413,420) = ( 413 × 420) / 7
LCM(413,420) = 173460 / 7
LCM(413,420) = 24780

1. What is the LCM of 413 and 420?

The LCM of 413 and 420 is 24780.

2. How to find the lowest common multiple of 413 and 420?

To find the lowest common multiple of 413 and 420, we have to get the multip;es of both numbers and identify the least common multiple in them which is 24780.

3. What are the Factors of 413?

Answer: Factors of 413 are 1, 7, 59, 413. There are 4 integers that are factors of 413. The greatest factor of 413 is 413.

4. What are the Factors of 420?

Answer: Factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420. There are 24 integers that are factors of 420. The greatest factor of 420 is 420.

Answer:

Least Common Multiple of 413 and 420 = 24780

Step 1: Find the prime factorization of 413

413 = 7 x 59

Step 2: Find the prime factorization of 420

420 = 2 x 2 x 3 x 5 x 7

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

LCM = 24780 = 2 x 2 x 3 x 5 x 7 x 59

Step 4: Therefore, the least common multiple of 413 and 420 is 24780.