Samaira writes 6 pages in one hour, Kate writes 12 pages in one hour whereas Maggie writes 8 pages in one hour. Find the least number of pages that they can write in minimum time if they have to write equal number of pages (The time taken by them should be in whole numbers).

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Solution

The correct option is B 24
The least number of pages to be written can be obtained by finding the LCM of the number of pages that they write in an hour.

Samaira writes 6 pages
Kate writes 12 and
Maggie writes 8.

LCM of 6, 12 and 8 by prime factorisation method:

6 = 2 × 3
12 = 2 × 2 × 3
8 = 2 × 2 × 2
The LCM of two numbers is the product of the prime factors
counted the maximum number of times they occur in prime factorisation of any of the numbers.

2 occurs thrice.
3 occurs once.

LCM will be 2 × 2 × 2 × 3 = 24.

Therefore, they have to write 24 pages each.

(Then Samaira will take 4 hours, Kate will take 2 hours and Maggie will take 3 hours.)

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