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

Discussion :: Problems on H.C.F and L.C.M - General Questions (Q.No.30)

30. 

If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:

[A].
55
601
[B].
601
55
[C].
11
120
[D].
120
11

Answer: Option C

Explanation:

Let the numbers be a and b.

Then, a + b = 55 and ab = 5 x 120 = 600.

The required sum = 1 + 1 = a + b = 55 = 11
a b ab 600 120


M.V.Krishna said: (Mar 19, 2011)  
Its not clear for me, why the product of hcf and lcm are taken as ab.

Gurinder said: (May 1, 2011)  
@^^ Product of two numbers = Product of their H.C.F. and L.C.M.

Sonu Kumar said: (Aug 26, 2011)  
How product of two number will be its product of LCM and HCF?

Amol said: (Oct 4, 2011)  
Why 1/a + 1/b ?

Shiva said: (Nov 6, 2011)  
How product of two number will be its product of LCM and HCF?

Santosh Shegokar said: (May 24, 2012)  
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)

Arjunn said: (Mar 31, 2013)  
What is the hcf and lcm of 150, 210, 375?

Is the product of hcf and lcm equal to product of these 3 numbers?

Raj said: (Aug 1, 2013)  
How to find those two numbers?

Kishan said: (Sep 12, 2013)  
If HCF of two numbers is 98 and LCM of numbers is 2352 then what is the sum of these numbers?

Babita Loky said: (Apr 29, 2014)  
The hcf and lcm of two numbers are 4 and 48 respectively. One of the number is 12. Find the other number?

Tom said: (May 3, 2014)  
The sum of two numbers is 120 and their hcf is 12. Find the numbers?

Math_Lover said: (Jul 7, 2014)  
@Tom.

There are 2 answers for this:

12 and 108.
36 and 84.

Viswajith said: (Jan 31, 2015)  
The HCF of two numbers is 15. Find its LCM? Anyone please help with steps.

Jedi Knight Ani said: (Apr 10, 2015)  
@Amol.

Reciprocal is calculated by dividing 1 by that number. Sum of the reciprocals = 1/a + 1/b.

Narendra Pandey said: (Jun 24, 2015)  
@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.

Vighneshvinu said: (Nov 20, 2015)  
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.

Abhishek said: (Feb 5, 2016)  
Thanks it helped me a lot.

Kptel said: (Jun 8, 2016)  
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.

Alay Patel said: (Jun 20, 2016)  
If products of two numbers = products of HCF and LCM.

What if the sum of two numbers?

Surajit Halder said: (Jun 24, 2016)  
If the sum of two numbers is 110 and LCM of those two numbers are 300. Find two numbers?

Can anyone answer this question?

Sonu said: (Jul 9, 2016)  
How can we solve this? Let me know the method of solution.

Ankur said: (Jul 23, 2016)  
Guys! LCM * HFC = PRODUCT OF TWO NUMBERS. This is the rule.

Diviya Priya said: (Jul 31, 2016)  
If the sum of the 2 numbers is 220 and the LCM is 99. Then find the HCF?

Anisa said: (Aug 13, 2016)  
If LCM of two number is 729, then HCF is? Please give me the solution.

Deshraj said: (Aug 18, 2016)  
How can we find out the co-prime of any numeric number? Explain.

M Veeresh said: (Nov 5, 2016)  
@Anisa.

The Lcm of 2 numbers is 729. Find lcm to 729 it will be 81 then 81 * x = 729.

i.e. x = 81 then the other number is 9. i.e. 81, 9 HCF is 9.

Nirmala said: (Nov 21, 2016)  
Find the sum 7/16 + 5/24.

Give me the answer with the proper explanation.

Avhi said: (Dec 28, 2016)  
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.

Lucas said: (Feb 14, 2017)  
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.

Subasini Barik said: (Oct 14, 2017)  
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.

Abhi said: (Nov 19, 2017)  
The product of two no=2448 and the difference of the two no is equal to their HCF and the HCF is a perfect square. Find the no?

Bhuttoo said: (Mar 7, 2018)  
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.

Milan said: (Oct 9, 2018)  
@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.

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