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Can some one pls explain this sum clearly since I am not able to understand even after seeing the soln. It's urgent pls...!!

Can some one pls explain this sum clearly since I am not able to understand even after seeing the soln. It's urgent pls...!! 

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Grade:10

2 Answers

Arun
25763 Points
2 years ago
Given that the smallest number when divided by 28 and 32 leaves remainder 8 and 12 respectively.
28 - 8 = 20 and 32 - 12 = 20 are divisible by the required numbers.

Therefore the required number will be 20 less than the LCM of 28 and 32.
Prime factorization of 28 = 2 * 2 * 7
Prime factorization of 32 = 2 * 2 * 2 * 2 * 2
LCM(28,32) = 2 * 2 * 2 * 2 * 2 * 7
                     = 224.

Therefore the required smallest number = 224 - 20
                                                                    = 204
 
Aariz Ahmed
31 Points
2 years ago
whats up buddy ?
i know this question is already answered but pls look at my solution too. imma explain it in the language of the people
so basically we have to find a number that when divided by 28 and 32 will leave remainder as 8 and 12
 we have to express a number on dividing by 2 other numbers will provide two remainders
so what we have to do s express the number as a product of its factors(read it again...itll make sense)
ie subtract the number with its remainder and then find lcm of the other numbers(ie 28 and 32)
therefore:
28-8=20 and 32-12=20
now find lcm of 28 and 32 that is equal to 224 
now subtract 224 with 20 cuz thats the least number that can be divisible by 28 and 32 to provide the remainders 8 and 12
therefore, the number is 204

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