A number K is such that when it is divided by 27,30 or 45,the remainder is 3. Find the smallest possible value of k.

Solution :-

First of all we have to find out the least common multiple of the given three numbers.

27 , 30 and 45

27 = 3 x 3 x 3

30 = 2 x 3 x 5

45 = 3 x 3 x 5

Form these factors we have to find the numbers which are common in all the three .

LCM = 2 x 3 x 3 x 3 x 5 = 270 .

Now 270 is completely divisible but the number which we want leaves 3 as remainder.

So adding 3 in 270 .

→ 273 is the required answer.

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