It is easy to find the LCM of 10 and 17 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 170 as output. Here you can check the answer for Find the LCM of 10 and 17.
Given Numbers are 10, 17
We can find the LCM of 10, 17 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 10 and 17
Multiples of 10 =10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,
Multiples of 17 =17,34,51,68,85,102,119,136,153,170,187,204,221,238,255,272,289,
Now, get the least common multiple of 10, 17 which is 170
So, the LCM of 10, 17 is 170.
One method for determining the LCM of 10 and 17 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 10's prime factorization:2 | 10 |
5 | 5 |
1 |
Prime factors of 10 are 2,5.
10 = 21×51
And this is 17's prime factorization:
17 | 17 |
1 |
Prime factors of 17 are 17.
17 = 171
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: 2,5,17
.21×51×171 = 170
This shows that the LCM of 10 and 17 is 170.
The first step in determining the Least Common Multiple of 10 and 17 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 10 and 17:
Lets look at the first ten multiples of these numbers, 10 and 17:
10,20,30,40,50,60,70,80,90,170 are the first ten multiples of 10.
17,34,51,68,85,102,119,136,153,289 are the first ten multiples of 17.
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 10 and 17, for example, are 120, 170, and 272. 170 is the least common multiple since it is the smallest.
10 and 17 have an LCM of 170.
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10 and 17, than apply into the LCM equation.
GCF(10,17) = 1
LCM(10,17) = ( 10 × 17) / 1
LCM(10,17) = 170 / 1
LCM(10,17) = 170
1. What is the LCM of 10 and 17?
The LCM of 10 and 17 is 170.
2. How to find the lowest common multiple of 10 and 17?
To find the lowest common multiple of 10 and 17, we have to get the multip;es of both numbers and identify the least common multiple in them which is 170.
3. What are the Factors of 10?
Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.
4. What are the Factors of 17?
Answer: Factors of 17 are 1, 17. There are 2 integers that are factors of 17. The greatest factor of 17 is 17.
5. How to Find the LCM of 10 and 17?Answer:
Least Common Multiple of 10 and 17 = 170
Step 1: Find the prime factorization of 10
10 = 2 x 5
Step 2: Find the prime factorization of 17
17 = 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 170 = 2 x 5 x 17
Step 4: Therefore, the least common multiple of 10 and 17 is 170.