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A heap of coconuts is divided into group...

A heap of coconuts is divided into groups of 2,3 and 5 and each time no coconut is left over. Find the least number of coconuts in the heap.

A

30

B

40

C

15

D

65

Text Solution

AI Generated Solution

The correct Answer is:
To find the least number of coconuts in the heap that can be divided into groups of 2, 3, and 5 without leaving any remainder, we will use the concept of Least Common Multiple (LCM). ### Step-by-Step Solution: 1. **Identify the numbers**: We need to find the LCM of the numbers 2, 3, and 5. 2. **List the multiples**: - Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, ... - Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ... - Multiples of 5: 5, 10, 15, 20, 25, 30, ... 3. **Find the common multiples**: The common multiples of 2, 3, and 5 from the lists above are: 30, 60, 90, ... 4. **Identify the least common multiple**: The smallest common multiple from the lists is 30. 5. **Conclusion**: Therefore, the least number of coconuts in the heap is **30**. ### Final Answer: The least number of coconuts in the heap is **30**. ---
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