A school in rural area has got very tiny classroom where a particular set of students are made to stand in rows of 8, 12 or 14 each. What will be the least number of students who can be occupied in the classroom?
Question
A school in rural area has got very tiny classroom where a particular set of students are made to stand in rows of 8, 12 or 14 each. What will be the least number of students who can be occupied in the classroom?
Solution
To find the least number of students who can be occupied in the classroom, we need to find the least common multiple (LCM) of the numbers 8, 12, and 14.
Step 1: First, let's find the prime factors of each number.
8 = 2 x 2 x 2 12 = 2 x 2 x 3 14 = 2 x 7
Step 2: Now, let's find the LCM. The LCM is found by multiplying the highest power of all the prime numbers together.
The highest power of 2 that appears in any of the factorizations is 2 x 2 x 2 (from 8). The highest power of 3 that appears is 3 (from 12). The highest power of 7 that appears is 7 (from 14).
Step 3: Multiply these together to get the LCM.
2 x 2 x 2 x 3 x 7 = 168
So, the least number of students who can be occupied in the classroom is 168.
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