Given Numbers are 416, 420

We can find the LCM of 416, 420 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 416 and 420

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

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 416, 420 which is 43680

So, the LCM of 416, 420 is 43680.

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

Prime factors of 416 are 2,13.

416 = 2⁵×13¹

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: 2,13, 3, 5,7

2⁵×3¹×5¹×7¹×13¹ = 43680

This shows that the LCM of 416 and 420 is 43680.

The first step in determining the Least Common Multiple of 416 and 420 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 416 and 420:

Lets look at the first ten multiples of these numbers, 416 and 420:

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

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 416 and 420, for example, are 4992, 7072, and 6720. 43680 is the least common multiple since it is the smallest.

416 and 420 have an LCM of 43680.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 416 and 420, than apply into the LCM equation.

GCF(416,420) = 4
LCM(416,420) = ( 416 × 420) / 4
LCM(416,420) = 174720 / 4
LCM(416,420) = 43680

1. What is the LCM of 416 and 420?

The LCM of 416 and 420 is 43680.

2. How to find the lowest common multiple of 416 and 420?

To find the lowest common multiple of 416 and 420, we have to get the multip;es of both numbers and identify the least common multiple in them which is 43680.

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 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 416 and 420 = 43680

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 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 = 43680 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 13

Step 4: Therefore, the least common multiple of 416 and 420 is 43680.