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Q.

The smallest 3 -digit number which is exactly divisible by 6,8 and 12  is ____.


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Detailed Solution

Concept- The smallest 3 -digit number which is exactly divisible by 6,8 and 12  is 120.
The integer must be divisible by 2 and 3 in order to be divided by 6. The criterion is that for an integer of 8, the last three digits must be divisible by 8. The integer must be divisible by 3 and 4 in order to be divided by 12.
So, we have to first find the LCM of 6,8 and 12. This is given by-
Question ImageThe LCM is the product of the prime factors obtained.
Question ImageNow let's determine the multiples of 24. Our final solution will be the first multiple that has three digits.
Question ImageQuestion ImageQuestion ImageQuestion ImageQuestion ImageTherefore, 120 is the smallest three-digit integer that is precisely divisible by 6, 8, and 12.
Hence, the correct answer is 120.
 Syllabus: CBSE
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