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

Thanks everyone for explaining.

Why they subtracted? Explain, please.

Thanks all for giving the clear explanation.

Why they took difference here? Anyone explain about it.

Same remainder means? Please anyone explain for me.

@Karthik V.

Great explanation, Thanks for solving this.

@All.

Here you need the highest common factor of three numbers those leave the same remainder

Let's do with the formula.

(p)q1 + r = 43.
(p)q2 + r = 91.
(p)q3 + r = 183.
we have used the same 'r' because all three leave the same remainder.
we need to find the 'p' value, which is the highest common factor.
to find the 'p' value, we need to remove 'r' first, ---------> (important point).
it seems that we can do it by making a difference between two equations.

Let's do it.

=> (pq2 +r) - (pq1 +r)
=> pq2+r-pq1-r
=> pq2-pq1 ----> now the reminder is taken out.
=> p(q2-q1) -----> need to find p value ----> (91-43)----> 1

Other numbers after diff will be like;

=> p(q3-q2) --------->(183-91)---------------> 2.
=> p(q3-q1) -------->(183-43) ---------------> 3.

Now we can find HCF of these three numbers to find p-value. Because 'p' is common in all numbers.

Hope you got it.

48 = 4 * 12
92 = 4 * 23
140 = 4 * 35.

1,2,3,5 prime numbers so 4 is the correct answer.

Do we know the number no let's assume the number is X therefore 43/X = 4 ithr for 43-4= 40 and similar to the all and by dividing we get reminder as 4.

Thanks for the explanation.