Problem Breakdown↵
1. 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]) ↵
2. Calculate Minimum Multiplier:↵
* For each pair (a[i], a[j]), find the smallest integer mmm 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.↵
3. Calculate the Cost:↵
* For each pair, compute the cost of the smallest multiplier mmm, which is simply the value of mmm.↵
* 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 leaves value of cost =12 for this pair similarly for others↵
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https://leetcode.com/discuss/interview-question/6029649/google-amaon
1. 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]) ↵
2. Calculate Minimum Multiplier:↵
* For each pair (a[i], a[j]), find the smallest integer mmm 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.↵
3. Calculate the Cost:↵
* For each pair, compute the cost of the smallest multiplier mmm, which is simply the value of mmm.↵
* 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 leaves value of cost =12 for this pair similarly for others↵
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https://leetcode.com/discuss/interview-question/6029649/google-amaon
