# JavaScript: K^{th} smallest number in a multiplication table

## JavaScript Math: Exercise-111 with Solution

Write a JavaScript program that creates a multiplication table of size m x n using integers where 1 <= k <= m * n. Return the kth smallest element in the said multiplication table.

In mathematics, a multiplication table is a mathematical table used to define a multiplication operation for an algebraic system.

The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations with base-ten numbers. Many educators believe it is necessary to memorize the table up to 9 x 9.

The illustration below shows a table up to 12 x 12, which is a size commonly used nowadays in English-world schools.

x |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |

0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

1 |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

2 |
0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |

3 |
0 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 |

4 |
0 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |

5 |
0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |

6 |
0 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 |

7 |
0 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |

8 |
0 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |

9 |
0 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 |

10 |
0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |

11 |
0 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 |

12 |
0 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 |

**Test Data:**

(3,3,8) -> 6

(2,3,4) -> 3

**Sample Solution:**

**JavaScript Code:**

```
/**
* Function to find the kth smallest element in the multiplication table of dimensions m x n.
* @param {number} m - The number of rows in the multiplication table.
* @param {number} n - The number of columns in the multiplication table.
* @param {number} k - The kth smallest element to find.
* @returns {number|boolean} - The kth smallest element if found, otherwise false.
*/
function test(m, n, k) {
// If k is less than 1 or greater than the total number of elements in the multiplication table, return false
if (k < 1 || k > m * n) return false;
var s = 1, p = n * m;
// Binary search to find the kth smallest element
while (s <= p) {
var mid = s + Math.floor((p - s) / 2);
var t = 0;
// Calculate the number of elements less than or equal to mid in the multiplication table
for (i = 1; i <= m; i++) {
t += Math.min(Math.floor(mid / i), n);
}
// Adjust the search range based on the value of t
if (t >= k) {
p = mid - 1;
} else {
s = mid + 1;
}
}
// Return the lower bound of the search range
return s;
}
// Test cases
m = 3;
n = 3;
k = 8;
console.log("m = " + m + " : n = " + n + ", k = " + k);
console.log("kth smallest element in m x n multiplication table: " + test(m, n, k));
m = 2;
n = 3;
k = 4;
console.log("m = " + m + " : n = " + n + ", k = " + k);
console.log("kth smallest element in m x n multiplication table: " + test(m, n, k));
```

Output:

m = 3 : n = 3, k = 8 kth smallest element in m x n multiplication table: 6 m = 2 : n = 3, k = 4 kth smallest element in m x n multiplication table: 3

**Flowchart: **

**Live Demo: **

See the Pen javascript-math-exercise-111 by w3resource (@w3resource) on CodePen.

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