Given Numbers are 461, 469

We can find the LCM of 461, 469 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 461 and 469

Multiples of 461 =461,922,1383,1844,2305,2766,3227,3688,4149,4610,5071,5532,5993,6454,6915,7376,7837,

Multiples of 469 =469,938,1407,1876,2345,2814,3283,3752,4221,4690,5159,5628,6097,6566,7035,7504,7973,

Now, get the least common multiple of 461, 469 which is 216209

So, the LCM of 461, 469 is 216209.

One method for determining the LCM of 461 and 469 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 461's prime factorization:

Prime factors of 461 are 461.

461 = 461¹

And this is 469's prime factorization:

Prime factors of 469 are 7,67.

469 = 7¹×67¹

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:461, 7,67

7¹×67¹×461¹ = 216209

This shows that the LCM of 461 and 469 is 216209.

The first step in determining the Least Common Multiple of 461 and 469 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 461 and 469:

Lets look at the first ten multiples of these numbers, 461 and 469:

461,922,1383,1844,2305,2766,3227,3688,4149,7837 are the first ten multiples of 461.

469,938,1407,1876,2345,2814,3283,3752,4221,7973 are the first ten multiples of 469.

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 461 and 469, for example, are 5532, 7837, and 7504. 216209 is the least common multiple since it is the smallest.

461 and 469 have an LCM of 216209.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 461 and 469, than apply into the LCM equation.

GCF(461,469) = 1
LCM(461,469) = ( 461 × 469) / 1
LCM(461,469) = 216209 / 1
LCM(461,469) = 216209

1. What is the LCM of 461 and 469?

The LCM of 461 and 469 is 216209.

2. How to find the lowest common multiple of 461 and 469?

To find the lowest common multiple of 461 and 469, we have to get the multip;es of both numbers and identify the least common multiple in them which is 216209.

3. What are the Factors of 461?

Answer: Factors of 461 are 1, 461. There are 2 integers that are factors of 461. The greatest factor of 461 is 461.

4. What are the Factors of 469?

Answer: Factors of 469 are 1, 7, 67, 469. There are 4 integers that are factors of 469. The greatest factor of 469 is 469.

Answer:

Least Common Multiple of 461 and 469 = 216209

Step 1: Find the prime factorization of 461

461 = 461

Step 2: Find the prime factorization of 469

469 = 7 x 67

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

LCM = 216209 = 7 x 67 x 461

Step 4: Therefore, the least common multiple of 461 and 469 is 216209.