Input: x = 15, y = 20, z = 100 Output: 60 Input: x = 30, y = 40, z = 400 Output: 120
One way to solve it is by finding GCD(x, y), and using it we find LCM(x, y). Similarly, we find LCM(x, z) and then we finally find the GCD of the obtained results.
An efficient approach can be done by the fact that the following version of distributivity holds true:
GCD(LCM (x, y), LCM (x, z)) = LCM(x, GCD(y, z))
For example, GCD(LCM(3, 4), LCM(3, 10)) = LCM(3, GCD(4, 10)) = LCM(3, 2) = 6
This reduces our work to compute the given problem statement.
As a side note, vice versa is also true, i.e., gcd(x, lcm(y, z)) = lcm(gcd(x, y), gcd(x, z)
This article is contributed by Mazhar Imam Khan. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
- Sum of the updated array after performing the given operation
- Remove an element to minimize the LCM of the given array
- Number of subarrays with GCD = 1 | Segment tree
- Find closest integer with the same weight
- Check whether the given decoded string is divisible by 6
- Find the minimum possible health of the winning player
- Construct an array from its pair-product
- Count of odd and even sum pairs in an array
- Smallest subarray with GCD as 1 | Segment Tree
- Number of ways to divide string in sub-strings such to make them in lexicographically increasing sequence
- Find Nth even length palindromic number formed using digits X and Y
- Minimum number to be added to all digits of X to make X > Y
- Cake Distribution Problem