Question

7. What is the smallest number that is divisible by 112, 84 and 96 leaving remainder? ​

Answer 1

Step-by-step explanation:

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Answer 2

We require to solve

x≡9mod112

x≡9mod280

From the first equation

x=112k+9

Putting this into the second equation

112k+9≡9mod280

⟹112k≡0mod280

⟹112k=280l

⟹2k=5l

This proves that 5l is even, but since 5 is odd, l is the even number

x=112k+9

⟹x=2k(56)+9

⟹x=5l(56)+9

Now we put l=0,2,4,…..

The least number is 9. This should be the answer. But to get to this, we don’t even have to make this big a solution.

The next number is for l=2 which gives

x=560+9=569

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