Mathematics
In the diagram below, Aditya has erased all the numbers except the common multiples. Fill in the missing numbers in the empty regions, if the highest number in the diagram is 30.
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Answer
The common multiples shown are 15 and 30. So the two circles represent multiples of two numbers whose common multiples (up to 30) include 15 and 30.
The two numbers must be factors of 15 (excluding 1 and 15 themselves, as the circles need separate non-common multiples in the highest range up to 30).
The factors of 15 are 1, 3, 5 and 15. So the two numbers are 3 and 5.
Multiples of 3 (up to 30, excluding common multiples): 3, 6, 9, 12, 18, 21, 24, 27.
Multiples of 5 (up to 30, excluding common multiples): 5, 10, 20, 25.
Common multiples (already given): 15, 30.
Hence, the left circle represents Multiples of 3 (containing 3, 6, 9, 12, 18, 21, 24, 27), the right circle represents Multiples of 5 (containing 5, 10, 20, 25), and the common region contains 15 and 30.
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