Find the least number which should be added to 2497
This question asks students to determine the smallest number that must be added to 2497 so that the resulting number becomes a perfect square. The solution involves identifying the next perfect square greater than 2497, calculating its square root, and finding the difference between the perfect square and the given number. This problem helps strengthen understanding of perfect squares, square roots, and number properties commonly covered in Class 8 Mathematics.
Question:
Find the least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3.
Solution:
We find the LCM of 5, 6, 4 and 3 first.
So, $\operatorname{LCM}(5,6,4,3)=2 \times 2 \times 3 \times 5=60$
Now, divide 2497 by 60, we get
To make the number completely divisible by 60, we must add a number that would make the remainder equal to 60.
Therefore, the number that must be added is 60
Hence, 23 must be added to 2497.
So, the number exactly divisible by 5, 6, 4 and 3 is 2497 + 23 = 2520