Given a number N(>=3). The task is to find the three integers (<=N) such that LCM of these three integers is maximum.
Input: N = 3 Output: 1 2 3 Input: N = 5 Output: 3 4 5
Approach: Since the task is to maximize the LCM, so if all three numbers don’t have any common factor then the LCM will be the product of those three numbers and that will be maximum.
- If n is odd then the answer will be n, n-1, n-2.
- If n is even,
- If gcd of n and n-3 is 1 then answer will be n, n-1, n-3.
- Otherwise, n-1, n-2, n-3 will be required answer.
Below is the implementation of the above approach:
11 10 9
- Sum of LCM(1, n), LCM(2, n), LCM(3, n), ... , LCM(n, n)
- Minimum replacement of pairs by their LCM required to reduce given array to its LCM
- Find the pair (a, b) with minimum LCM such that their sum is equal to N
- Number of pairs such that their HCF and LCM is equal
- Count of pairs upto N such whose LCM is not equal to their product for Q queries
- Find the number of positive integers less than or equal to N that have an odd number of digits
- Find the first N integers such that the sum of their digits is equal to 10
- Find any K distinct odd integers such that their sum is equal to N
- Count number of integers less than or equal to N which has exactly 9 divisors
- Sum of elements in 1st array such that number of elements less than or equal to them in 2nd array is maximum
- Count of integers of length N and value less than K such that they contain digits only from the given set
- Find two distinct numbers such that their LCM lies in given range
- Possible values of Q such that, for any value of R, their product is equal to X times their sum
- Find unique pairs such that each element is less than or equal to N
- Highest and Smallest power of K less than and greater than equal to N respectively
- Find maximum product of digits among numbers less than or equal to N
- Largest number with maximum trailing nines which is less than N and greater than N-D
- Numbers less than N that are perfect cubes and the sum of their digits reduced to a single digit is 1
- Find K consecutive integers such that their sum is N
- Maximum size of square such that all submatrices of that size have sum less than K
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