Given Numbers are 415, 420

We can find the LCM of 415, 420 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 415 and 420

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

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 415, 420 which is 34860

So, the LCM of 415, 420 is 34860.

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

Prime factors of 415 are 5,83.

415 = 5¹×83¹

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: 5,83, 2, 3,7

2²×3¹×5¹×7¹×83¹ = 34860

This shows that the LCM of 415 and 420 is 34860.

The first step in determining the Least Common Multiple of 415 and 420 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 415 and 420:

Lets look at the first ten multiples of these numbers, 415 and 420:

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

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 415 and 420, for example, are 4980, 7055, and 6720. 34860 is the least common multiple since it is the smallest.

415 and 420 have an LCM of 34860.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 415 and 420, than apply into the LCM equation.

GCF(415,420) = 5
LCM(415,420) = ( 415 × 420) / 5
LCM(415,420) = 174300 / 5
LCM(415,420) = 34860

1. What is the LCM of 415 and 420?

The LCM of 415 and 420 is 34860.

2. How to find the lowest common multiple of 415 and 420?

To find the lowest common multiple of 415 and 420, we have to get the multip;es of both numbers and identify the least common multiple in them which is 34860.

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 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 415 and 420 = 34860

Step 1: Find the prime factorization of 415

415 = 5 x 83

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 = 34860 = 2 x 2 x 3 x 5 x 7 x 83

Step 4: Therefore, the least common multiple of 415 and 420 is 34860.