LCM of 34 and 40
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 34 and 40 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 680 as output. Here you can check the answer for Find the LCM of 34 and 40.
What is LCM of 34 and 40
Given Numbers are 34, 40
We can find the LCM of 34, 40 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 34 and 40
Multiples of 34 =34,68,102,136,170,204,238,272,306,340,374,408,442,476,510,544,578,
Multiples of 40 =40,80,120,160,200,240,280,320,360,400,440,480,520,560,600,640,680,
Now, get the least common multiple of 34, 40 which is 680
So, the LCM of 34, 40 is 680.
Least Common Multiple (LCM) of 34 and 40 with the help of Prime Factorisation
One method for determining the LCM of 34 and 40 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 34's prime factorization:
| 2 | 34 |
| 17 | 17 |
| 1 |
Prime factors of 34 are 2,17.
34 = 21×171
And this is 40's prime factorization:
| 2 | 40 |
| 2 | 20 |
| 2 | 10 |
| 5 | 5 |
| 1 |
Prime factors of 40 are 2,5.
40 = 23×51
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: 2,17,5
.23×51×171 = 680
This shows that the LCM of 34 and 40 is 680.
How to Calculate the LCM of 34 and 40 Using Common Multiples
The first step in determining the Least Common Multiple of 34 and 40 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 34 and 40:
Lets look at the first ten multiples of these numbers, 34 and 40:
34,68,102,136,170,204,238,272,306,578 are the first ten multiples of 34.
40,80,120,160,200,240,280,320,360,680 are the first ten multiples of 40.
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 34 and 40, for example, are 408, 578, and 640. 680 is the least common multiple since it is the smallest.
34 and 40 have an LCM of 680.
Least Common Multiple of 34 and 40 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34 and 40, than apply into the LCM equation.
GCF(34,40) = 2
LCM(34,40) = ( 34 × 40) / 2
LCM(34,40) = 1360 / 2
LCM(34,40) = 680
Related Least Common Multiples of 34
Related Least Common Multiples of 40
Frequently Asked Questions on LCM of 34 and 40
1. What is the LCM of 34 and 40?
The LCM of 34 and 40 is 680.
2. How to find the lowest common multiple of 34 and 40?
To find the lowest common multiple of 34 and 40, we have to get the multip;es of both numbers and identify the least common multiple in them which is 680.
3. What are the Factors of 34?
Answer: Factors of 34 are 1, 2, 17, 34. There are 4 integers that are factors of 34. The greatest factor of 34 is 34.
4. What are the Factors of 40?
Answer: Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. There are 8 integers that are factors of 40. The greatest factor of 40 is 40.
5. How to Find the LCM of 34 and 40?Answer:
Least Common Multiple of 34 and 40 = 680
Step 1: Find the prime factorization of 34
34 = 2 x 17
Step 2: Find the prime factorization of 40
40 = 2 x 2 x 2 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 = 680 = 2 x 2 x 2 x 5 x 17
Step 4: Therefore, the least common multiple of 34 and 40 is 680.