Given Numbers are 456, 462

We can find the LCM of 456, 462 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 456 and 462

Multiples of 456 =456,912,1368,1824,2280,2736,3192,3648,4104,4560,5016,5472,5928,6384,6840,7296,7752,

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

Now, get the least common multiple of 456, 462 which is 35112

So, the LCM of 456, 462 is 35112.

One method for determining the LCM of 456 and 462 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 456's prime factorization:

Prime factors of 456 are 2, 3,19.

456 = 2³×3¹×19¹

And this is 462's prime factorization:

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

462 = 2¹×3¹×7¹×11¹

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, 3,19, 7,11

2³×3¹×7¹×11¹×19¹ = 35112

This shows that the LCM of 456 and 462 is 35112.

The first step in determining the Least Common Multiple of 456 and 462 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 456 and 462:

Lets look at the first ten multiples of these numbers, 456 and 462:

456,912,1368,1824,2280,2736,3192,3648,4104,7752 are the first ten multiples of 456.

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

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 456 and 462, for example, are 5472, 7752, and 7392. 35112 is the least common multiple since it is the smallest.

456 and 462 have an LCM of 35112.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 456 and 462, than apply into the LCM equation.

GCF(456,462) = 6
LCM(456,462) = ( 456 × 462) / 6
LCM(456,462) = 210672 / 6
LCM(456,462) = 35112

1. What is the LCM of 456 and 462?

The LCM of 456 and 462 is 35112.

2. How to find the lowest common multiple of 456 and 462?

To find the lowest common multiple of 456 and 462, we have to get the multip;es of both numbers and identify the least common multiple in them which is 35112.

3. What are the Factors of 456?

Answer: Factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456. There are 16 integers that are factors of 456. The greatest factor of 456 is 456.

4. 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.

Answer:

Least Common Multiple of 456 and 462 = 35112

Step 1: Find the prime factorization of 456

456 = 2 x 2 x 2 x 3 x 19

Step 2: Find the prime factorization of 462

462 = 2 x 3 x 7 x 11

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

LCM = 35112 = 2 x 2 x 2 x 3 x 7 x 11 x 19

Step 4: Therefore, the least common multiple of 456 and 462 is 35112.