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 a pair with maximum product in array of Integers
- Find integers that divides maximum number of elements of the array
- 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 four factors of N with maximum product and sum equal to N | Set-2
- Find maximum product of digits among numbers less than or equal to N
- Check if the sum of distinct digits of two integers are equal
- Count number of integers less than or equal to N which has exactly 9 divisors
- Maximum GCD of N integers with given product
- Count positive integers with 0 as a digit and maximum 'd' digits
- Maximum Primes whose sum is equal to given N
- Find N integers with given difference between product and sum
- Find the number of integers from 1 to n which contains digits 0's and 1's only
- Maximum length subarray with LCM equal to product
- Maximum elements that can be made equal with k updates
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