Given Numbers are 420, 428

We can find the LCM of 420, 428 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 420 and 428

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

Multiples of 428 =428,856,1284,1712,2140,2568,2996,3424,3852,4280,4708,5136,5564,5992,6420,6848,7276,

Now, get the least common multiple of 420, 428 which is 44940

So, the LCM of 420, 428 is 44940.

One method for determining the LCM of 420 and 428 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 420's prime factorization:

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

420 = 2²×3¹×5¹×7¹

And this is 428's prime factorization:

Prime factors of 428 are 2,107.

428 = 2²×107¹

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, 3, 5,7,107

2²×3¹×5¹×7¹×107¹ = 44940

This shows that the LCM of 420 and 428 is 44940.

The first step in determining the Least Common Multiple of 420 and 428 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 420 and 428:

Lets look at the first ten multiples of these numbers, 420 and 428:

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

428,856,1284,1712,2140,2568,2996,3424,3852,7276 are the first ten multiples of 428.

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 420 and 428, for example, are 5040, 7140, and 6848. 44940 is the least common multiple since it is the smallest.

420 and 428 have an LCM of 44940.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 420 and 428, than apply into the LCM equation.

GCF(420,428) = 4
LCM(420,428) = ( 420 × 428) / 4
LCM(420,428) = 179760 / 4
LCM(420,428) = 44940

1. What is the LCM of 420 and 428?

The LCM of 420 and 428 is 44940.

2. How to find the lowest common multiple of 420 and 428?

To find the lowest common multiple of 420 and 428, we have to get the multip;es of both numbers and identify the least common multiple in them which is 44940.

3. 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.

4. What are the Factors of 428?

Answer: Factors of 428 are 1, 2, 4, 107, 214, 428. There are 6 integers that are factors of 428. The greatest factor of 428 is 428.

Answer:

Least Common Multiple of 420 and 428 = 44940

Step 1: Find the prime factorization of 420

420 = 2 x 2 x 3 x 5 x 7

Step 2: Find the prime factorization of 428

428 = 2 x 2 x 107

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

LCM = 44940 = 2 x 2 x 3 x 5 x 7 x 107

Step 4: Therefore, the least common multiple of 420 and 428 is 44940.