Question

find the largest number that will divide 398 and 436 and 542 leaving remainders 7 and 11 and 15 respectively

Answer 1

The required number is L.C.M. of (398-7)=391, (436-11)=425 and (542-15)=527.
I think their L.C.M. should be 17.
So,your answer will be 17.

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Answer 2

Given :-

398 , 436 and 542

To Find :-

The largest number

Solution :-

Let’s assume the integer is x

According to the condition given in the question

⇒ xy+7 = 398

⇒  xz+11 = 436

⇒  xk+15 = 542

⇒ xy =391

⇒  xz = 425

⇒  xk = 527

⇒  17 × 23 = 391

⇒  17 × 25 = 425

⇒ 17 × 31 = 527

So, the largest possible integer that will divide 398,436,542 & leaves reminder 7,11 and 15 respectively was 17.