A number leaves a remainder of 2 and 4 respectively when divided by 4 and 5. Find the least three digit such number.
Explanation:
Let the number be N.
∴ N = 4a + 2 i.e., N can be 2, 6, 10, 14, 18, ….
Also, N = 5b + 4 i.e., N can be 4, 9, 14, 19, …
The least possible value of N = 14.
∴ N = k × LCM(4, 5) + 14 = 20k + 14.
Now we have to find the least three-digit such number.
For k = 5, N = 114 (least three-digit such number).
Hence, 114.
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