Aptitude - Problems on H.C.F and L.C.M - Discussion

Here in this question greatest number is 7 and it gives the same remainder that is 1 when divided by all. So how is the answer 4?

In @Prasanth answer, p is the divisor not dividend and the analysis of sum is correct.

Yes your right @Sowjanya. But @Prasanth is almost right I think you need more information.

1st divide 48 with 4 then remainder is 0.

2nd divide 92 with 4 then remainder is 0.

3rd divide 140 with 4 then remainder is 0.

Hence so 4 is a perfect number.

Easy calculation, 7 and 13 are directly eliminated.

4 and 9 are the required. So divide it by the 9, no remainder will be same. So 4 is the option.

How to solve the same question if remainder is not same in each case?

I can't understand the question.

An indirect way to understand.

Let's take the numbers are 28, 35, 56 and the divisor is 7.

When 7 divide these remainder are 0, 0, 0.

Now see 35 - 28 = 7, (Divisible by divisor). Also 56 - 28 = 28 and 56 - 35 = 21 both are divided by divisor. This is like property check for any number.

So we can use this in our problem. Two or more no. when giving the same remainder with common divisor then the difference between the original numbers are also divided by divisor.

Further using in question. 91, 43, 183. See we don't have divisor or factor.

See d or factor divide the no 91, 43, 183 and the differences.

91 - 43, 183 - 43, 183 - 91 say 48, 140, 92.

Since any common divisor or heresy HCF should divide the numbers and differences so we find the HCF of 48, 140, 92.

Hope this will clear why we take difference.

Dear friends, I am trying to satisfy this question, that why we have to take differences of those numbers.

We all know that the result of H.C.F of any two or more numbers is only their difference between them, such as H.C.F. OF 7& 14 = 7.

Now we calculate the H.C.F. of 7, 14 &21.
We see that the differences between them are actually (14 - 7 = 7, 21 - 7 = 7 & 21 - 7=14.

But the difference of 21 - 7 = 14, whose factor is 2 & 7.

Hence, only 7 will be the H.C.F. OF 7, 14 & 21.
On the above basis, the difference between them is 48, 92 & 140.

Therefore, the H.C.F.of 48, 92 & 140 will be 4.

Hi, how to solve the Lcm? Please help me.