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
- Find the first N integers such that the sum of their digits is equal to 10
- Find a pair with maximum product in array of Integers
- Find integers that divides maximum number of elements of the array
- Find the number of positive integers less than or equal to N that have an odd number of digits
- Find four factors of N with maximum product and sum equal to N | Set-2
- Find four factors of N with maximum product and sum equal to N
- Find four factors of N with maximum product and sum equal to N | Set 3
- Find maximum product of digits among numbers less than or equal to N
- Remove two consecutive integers from 1 to N to make sum equal to S
- Count number of integers less than or equal to N which has exactly 9 divisors
- Check if the sum of distinct digits of two integers are equal
- Check if N rectangles of equal area can be formed from (4 * N) integers
- Maximum GCD of N integers with given product
- Maximum of all the integers in the given level of Pascal triangle
- Count positive integers with 0 as a digit and maximum 'd' digits
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