Question

find the smallest number that can be divided by 254 and 508 which leaves the remainder 4

508
516
512
520​

Answer 1

Answer:

when we divide 508 with 512 then the reminder is 4 and when divide 254 with 512 then also reminder is 4

therefore the answer of this question is 512

Answer 2

The smallest number that can be divided by 254 and 508 which leaves the remainder 4 is 512. Thus Option C is correct

Solution:

To find the smallest number we have to find the LCM of 254 and 508 which is as follows:

Let us first find the prime factors of 254 and 508

$\begin{array}{l}{254=2 \times 127} \\\\ {508=2 \times 2 \times 127}\end{array}$

First list the prime factors of 254 and 508

Then multiply each factor the greatest number of times it occurs in either number.

If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

So by above definition, we get

L.C.M(254 and 508) $=2 \times 2 \times 127=508$

508 is a number which completely divides both 254 and 508

To get a number which gives a remainder of 4 we have to add 4 to the smallest number we obtain .i.e.508 + 4 = 512

So, the required smallest number which when divided by 254 and 508 gives a remainder of 4 is 512

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