Problem Breakdown
- Find LCM for Each Pair:
- For each unique pair (a[i], a[j]) in the array a, compute the Least Common Multiple (LCM).
- The pairs include (a[i], a[i]) for each single number, as well as every combination of distinct numbers (a[i], a[j])
- Calculate Minimum Multiplier:
- For each pair (a[i], a[j]), find the smallest integer m such that: LCM(a[i],a[j])×m≥k
{LCM}(a[i], a[j]) * m .= k LCM(a[i],a[j])×m≥k
- This product should also be a multiple of k.
- Calculate the Cost:
- For each pair, compute the cost of the smallest multiplier m, which is simply the value of m.
- Sum up the costs for all pairs to get the total answer.
eg: [4,5,6] k=12 ans=>3+12+2+2*(3+2+1)=29, give a complexity less than O(N2) less than 108 as n<=10**5
pairs->(4,4) ,(5,5,) ,(6,6) ,(4,5) ,(5,4) ,(5,6) ,(6,5) , (4,6), (6,4)
so(lcm(5,5))=5*12=60 multiple of k leavse value of cost =12 for this pair similarly for others