Question

smallest nuber divisible by 15,20,25,30 leaves 5 as remainder

Answer 1

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Answer 2

Given numbers are :- 15 , 20 , 25 , 30

Now :-

To find the smallest number that divides 15 , 20 , 25 , 30 and leaves 5 remainder 5 in each case :-

at first , we will subtract 5 from the given number .

Then :-

we have to find the hcf of the resulting number :-

In order to obtain the required number .

Now :-

15 - 5 = 10

20 - 5 = 15

25 - 5 = 20

30 - 5 = 25

Now :-

Prime factorisation of 10 , 15 , 20 , 25 .

10 = 2 × 5

15 = 3 × 5

20 = 2 × 2 × 5

25 = 5 × 5

HCF = 5

Hence :-

The smallest number that divides 10 , 15 , 20 , 25 and leaves remainder 5 in each case is 5 .

Answer :-

The smallest number is 5 .