It is easy to find the LCM of 224 and 225 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 50400 as output. Here you can check the answer for Find the LCM of 224 and 225.
Given Numbers are 224, 225
We can find the LCM of 224, 225 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 224 and 225
Multiples of 224 =224,448,672,896,1120,1344,1568,1792,2016,2240,2464,2688,2912,3136,3360,3584,3808,
Multiples of 225 =225,450,675,900,1125,1350,1575,1800,2025,2250,2475,2700,2925,3150,3375,3600,3825,
Now, get the least common multiple of 224, 225 which is 50400
So, the LCM of 224, 225 is 50400.
One method for determining the LCM of 224 and 225 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 224's prime factorization:2 | 224 |
2 | 112 |
2 | 56 |
2 | 28 |
2 | 14 |
7 | 7 |
1 |
Prime factors of 224 are 2,7.
224 = 25×71
And this is 225's prime factorization:
3 | 225 |
3 | 75 |
5 | 25 |
5 | 5 |
1 |
Prime factors of 225 are 3,5.
225 = 32×52
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: 2,7, 3,5
.25×32×52×71 = 50400
This shows that the LCM of 224 and 225 is 50400.
The first step in determining the Least Common Multiple of 224 and 225 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 224 and 225:
Lets look at the first ten multiples of these numbers, 224 and 225:
224,448,672,896,1120,1344,1568,1792,2016,3808 are the first ten multiples of 224.
225,450,675,900,1125,1350,1575,1800,2025,3825 are the first ten multiples of 225.
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 224 and 225, for example, are 2688, 3808, and 3600. 50400 is the least common multiple since it is the smallest.
224 and 225 have an LCM of 50400.
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 224 and 225, than apply into the LCM equation.
GCF(224,225) = 1
LCM(224,225) = ( 224 × 225) / 1
LCM(224,225) = 50400 / 1
LCM(224,225) = 50400
1. What is the LCM of 224 and 225?
The LCM of 224 and 225 is 50400.
2. How to find the lowest common multiple of 224 and 225?
To find the lowest common multiple of 224 and 225, we have to get the multip;es of both numbers and identify the least common multiple in them which is 50400.
3. What are the Factors of 224?
Answer: Factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224. There are 12 integers that are factors of 224. The greatest factor of 224 is 224.
4. What are the Factors of 225?
Answer: Factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225. There are 9 integers that are factors of 225. The greatest factor of 225 is 225.
5. How to Find the LCM of 224 and 225?Answer:
Least Common Multiple of 224 and 225 = 50400
Step 1: Find the prime factorization of 224
224 = 2 x 2 x 2 x 2 x 2 x 7
Step 2: Find the prime factorization of 225
225 = 3 x 3 x 5 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 50400 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 7
Step 4: Therefore, the least common multiple of 224 and 225 is 50400.