Given Numbers are 462, 470

We can find the LCM of 462, 470 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 462 and 470

Multiples of 462 =462,924,1386,1848,2310,2772,3234,3696,4158,4620,5082,5544,6006,6468,6930,7392,7854,

Multiples of 470 =470,940,1410,1880,2350,2820,3290,3760,4230,4700,5170,5640,6110,6580,7050,7520,7990,

Now, get the least common multiple of 462, 470 which is 108570

So, the LCM of 462, 470 is 108570.

One method for determining the LCM of 462 and 470 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 462's prime factorization:

Prime factors of 462 are 2, 3, 7,11.

462 = 2¹×3¹×7¹×11¹

And this is 470's prime factorization:

Prime factors of 470 are 2, 5,47.

470 = 2¹×5¹×47¹

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, 7,11, 5,47

2¹×3¹×5¹×7¹×11¹×47¹ = 108570

This shows that the LCM of 462 and 470 is 108570.

The first step in determining the Least Common Multiple of 462 and 470 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 462 and 470:

Lets look at the first ten multiples of these numbers, 462 and 470:

462,924,1386,1848,2310,2772,3234,3696,4158,7854 are the first ten multiples of 462.

470,940,1410,1880,2350,2820,3290,3760,4230,7990 are the first ten multiples of 470.

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 462 and 470, for example, are 5544, 7854, and 7520. 108570 is the least common multiple since it is the smallest.

462 and 470 have an LCM of 108570.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 462 and 470, than apply into the LCM equation.

GCF(462,470) = 2
LCM(462,470) = ( 462 × 470) / 2
LCM(462,470) = 217140 / 2
LCM(462,470) = 108570

1. What is the LCM of 462 and 470?

The LCM of 462 and 470 is 108570.

2. How to find the lowest common multiple of 462 and 470?

To find the lowest common multiple of 462 and 470, we have to get the multip;es of both numbers and identify the least common multiple in them which is 108570.

3. What are the Factors of 462?

Answer: Factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462. There are 16 integers that are factors of 462. The greatest factor of 462 is 462.

4. What are the Factors of 470?

Answer: Factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470. There are 8 integers that are factors of 470. The greatest factor of 470 is 470.

Answer:

Least Common Multiple of 462 and 470 = 108570

Step 1: Find the prime factorization of 462

462 = 2 x 3 x 7 x 11

Step 2: Find the prime factorization of 470

470 = 2 x 5 x 47

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

LCM = 108570 = 2 x 3 x 5 x 7 x 11 x 47

Step 4: Therefore, the least common multiple of 462 and 470 is 108570.