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

Dear @Kishan you will require options to find the answer for if HCF of two numbers is 98 and LCM of numbers is 2352 then what is the sum of these numbers?

From the options find a number which is divisible by 98. Which will be your required answer? Example 1372, 1398, 1426, 1484.

Out of these options a number which is exactly divisible by 98 is 1372.

So this will be your required answer (HCF is a common factor for both the numbers. So if x & y are the nos then the sum will be x+y = 98*(a+b). Here x = 98*a & y = 98*b).

Hope this was useful to you.

@Vishwajit.

As HCF and LCM is given.

Standard Formula:

Product of two number = HCF*LCM.

Suppose two number be x and y.

xy = 5*12.
x+y = 55.

Now x = 55-y put the value of x in xy = 600.

Now (55-y)y = 600.
y^2-55y+600 = 0.

By factorization we get.

y^2-40y-15y+600 = 0.
y(y-40)-15(y-40) = 0.

Now y=40 and 14.

As in question reciprocal of number 1/x+1/y.

1/40+1/15 = 55/600 = 11/120.

That's it.

This is standard formula.
Product of any two numbers = product of their LCM and HCF
We have been asked to find the sum of reciprocals of the said numbers.
Here let number be a and b
Hence as per above formula a*b = HCF *LCM = 5 *120 =600
And also given a+b = 55.
Now reciprocals of above number will be 1/a and 1/b
Hence (1/a)+(1/b)= (a+b)/a*b= 55/600 = 11/120 (answer)

Let the number be 5a and 5b.
Given HCF= 5 LCM =120.
Sum=55.
5a+5b=55.
=> a+b=11 ------> (1)

By property product of numbers= LCM*HCF.
5a*5b= 5*120
=> 5ab= 120 --------> (2).

Now sum of reciprocal of numbers:-
(1/5a) + (1/5b) = a+b/5ab.
Putting values from (1) and (2).
(1/5a) + (1/5b)= 11/120.

Please, anyone help me to solve this question for me.

Two bulbs flash at regular intervals of 30 and 36 seconds respectively. They flash together at 10.45. At what time will they flash together?

(a) a second time.

(b) a 5th time.

@Bhuttoo & @Lucas.

1st of all you should find the lcm that is 180 second or 3 minutes. It means they flash together at every 3miunites.

They will flash together.
(a) at 10:48 for the second time.
(b) at 11:00 for 5th time.

Please solve this question for me.

Two bulbs flash at regular intervals of 30 and 36 seconds respectively. They flash together at 10.45. At what time will they flash together?

(a) a second time.
(b) a 5th time.

If no's are 40 &15 what will be the sum of their reciprocals with the same condition?

And please tell me what would be the HCF if sum of their reciprocals is 11/120?

Please anyone answer this.

Two numbers are in the ratio of 5: 8. If 12 is added to each, they are in the ratio of 3: 4. Find the sum of two numbers? Please give me the answer and explanation.

The product of LCM and HCF of two no is 24 and the difference of two no is 2 then find the sum of two no?

Please give me the solution for this question.