Given Numbers are 450, 456

We can find the LCM of 450, 456 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 450 and 456

Multiples of 450 =450,900,1350,1800,2250,2700,3150,3600,4050,4500,4950,5400,5850,6300,6750,7200,7650,

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

Now, get the least common multiple of 450, 456 which is 34200

So, the LCM of 450, 456 is 34200.

One method for determining the LCM of 450 and 456 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 450's prime factorization:

Prime factors of 450 are 2, 3,5.

450 = 2¹×3²×5²

And this is 456's prime factorization:

Prime factors of 456 are 2, 3,19.

456 = 2³×3¹×19¹

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, 3,5,19

2³×3²×5²×19¹ = 34200

This shows that the LCM of 450 and 456 is 34200.

The first step in determining the Least Common Multiple of 450 and 456 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 450 and 456:

Lets look at the first ten multiples of these numbers, 450 and 456:

450,900,1350,1800,2250,2700,3150,3600,4050,7650 are the first ten multiples of 450.

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

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 450 and 456, for example, are 5400, 7650, and 7296. 34200 is the least common multiple since it is the smallest.

450 and 456 have an LCM of 34200.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 450 and 456, than apply into the LCM equation.

GCF(450,456) = 6
LCM(450,456) = ( 450 × 456) / 6
LCM(450,456) = 205200 / 6
LCM(450,456) = 34200

1. What is the LCM of 450 and 456?

The LCM of 450 and 456 is 34200.

2. How to find the lowest common multiple of 450 and 456?

To find the lowest common multiple of 450 and 456, we have to get the multip;es of both numbers and identify the least common multiple in them which is 34200.

3. What are the Factors of 450?

Answer: Factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450. There are 18 integers that are factors of 450. The greatest factor of 450 is 450.

4. 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.

Answer:

Least Common Multiple of 450 and 456 = 34200

Step 1: Find the prime factorization of 450

450 = 2 x 3 x 3 x 5 x 5

Step 2: Find the prime factorization of 456

456 = 2 x 2 x 2 x 3 x 19

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

LCM = 34200 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 19

Step 4: Therefore, the least common multiple of 450 and 456 is 34200.