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Given:
The expanded form of is
.
Where, s, t, K are positive integers.
To find:
The smallest possible value of K.
Solution:
The expanded form of is
. It means,
On comping both sides, we get
...(i)
K is a positive integer if s>t.
And
The factor pairs of 40 are (1,40), (2,20), (4,10), (5,8), (8,5), (10,4), (20,2) and (40,1).
Since s>t, therefore the possible values for (s,t) are (8,5), (10,4), (20,2) and (40,1).
Using (i), find the value of K for each factor pair.
Therefore, the smallest possible value of K is 3.