Given Numbers are 420, 426

We can find the LCM of 420, 426 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 420 and 426

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

Multiples of 426 =426,852,1278,1704,2130,2556,2982,3408,3834,4260,4686,5112,5538,5964,6390,6816,7242,

Now, get the least common multiple of 420, 426 which is 29820

So, the LCM of 420, 426 is 29820.

One method for determining the LCM of 420 and 426 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 426's prime factorization:

Prime factors of 426 are 2, 3,71.

426 = 2¹×3¹×71¹

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, 5,7,71

2²×3¹×5¹×7¹×71¹ = 29820

This shows that the LCM of 420 and 426 is 29820.

The first step in determining the Least Common Multiple of 420 and 426 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 420 and 426:

Lets look at the first ten multiples of these numbers, 420 and 426:

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

426,852,1278,1704,2130,2556,2982,3408,3834,7242 are the first ten multiples of 426.

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 426, for example, are 5040, 7140, and 6816. 29820 is the least common multiple since it is the smallest.

420 and 426 have an LCM of 29820.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 420 and 426, than apply into the LCM equation.

GCF(420,426) = 6
LCM(420,426) = ( 420 × 426) / 6
LCM(420,426) = 178920 / 6
LCM(420,426) = 29820

1. What is the LCM of 420 and 426?

The LCM of 420 and 426 is 29820.

2. How to find the lowest common multiple of 420 and 426?

To find the lowest common multiple of 420 and 426, we have to get the multip;es of both numbers and identify the least common multiple in them which is 29820.

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 426?

Answer: Factors of 426 are 1, 2, 3, 6, 71, 142, 213, 426. There are 8 integers that are factors of 426. The greatest factor of 426 is 426.

Answer:

Least Common Multiple of 420 and 426 = 29820

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 426

426 = 2 x 3 x 71

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

LCM = 29820 = 2 x 2 x 3 x 5 x 7 x 71

Step 4: Therefore, the least common multiple of 420 and 426 is 29820.