Aptitude - Problems on H.C.F and L.C.M - Discussion
Discussion Forum : Problems on H.C.F and L.C.M - General Questions (Q.No. 7)
7.
Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
Answer: Option
Explanation:
Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.
Discussion:
41 comments Page 3 of 5.
Pappu said:
10 years ago
Simply explain what is L.C.M and H.C.F please?
Jahulhak said:
10 years ago
3*4*5-60 = 2400/60.
= 40 answer.
= 40 answer.
Karthick said:
10 years ago
First we have to find original nos.
L.C.M = 2400.
Ratio = 3:4:5.
2400/3 = 800.
2400/4 = 600.
2400/5 = 480.
L.C.M of 800, 600, 480 = 40.
L.C.M = 2400.
Ratio = 3:4:5.
2400/3 = 800.
2400/4 = 600.
2400/5 = 480.
L.C.M of 800, 600, 480 = 40.
Sundar said:
10 years ago
3x*4x*5x=2400x.
1x gets cancelled.
Then 60x^2=2400;
x^2=40.
Then x is 2 root 10; Answer is wrong.
1x gets cancelled.
Then 60x^2=2400;
x^2=40.
Then x is 2 root 10; Answer is wrong.
(1)
Jayakrishna vinod said:
1 decade ago
What is the use of LCM & HCF in our day to day life?
Paridhi said:
1 decade ago
Why is LCM 3x X 4x X 5x is the LCM equal to the product of the numbers?
Varun said:
1 decade ago
Its wrong. LCM * HCF = product of numbers is only valid for 2 numbers.
Consider an example for no 2, 15, 20;
LCM = 2*2*3*5 = 60.
While HCF of these two numbers is 1.
Now as per your logic LCM*HCF = product of 2 numbers.
Hence as per this:
60*1 = 2*15*20.
60 != 600.
Hence your logic is invalid please help regarding that.
Consider an example for no 2, 15, 20;
LCM = 2*2*3*5 = 60.
While HCF of these two numbers is 1.
Now as per your logic LCM*HCF = product of 2 numbers.
Hence as per this:
60*1 = 2*15*20.
60 != 600.
Hence your logic is invalid please help regarding that.
Sunil sharma said:
1 decade ago
3*40 = 120.
4*40 = 160.
5*40 = 200.
So number is 120, 160, 200.
We are calculate LCM above three number = 2400.
Do answer is 40.
4*40 = 160.
5*40 = 200.
So number is 120, 160, 200.
We are calculate LCM above three number = 2400.
Do answer is 40.
Aman Kaushik said:
1 decade ago
Ratio 3:4:5
LCM 2400.
HCF ?
Solve answer = 3*4*5 = 60.
LCM is = 2400.
HCF IS = 2400/60.
= 40.
LCM 2400.
HCF ?
Solve answer = 3*4*5 = 60.
LCM is = 2400.
HCF IS = 2400/60.
= 40.
Harry said:
1 decade ago
I did like this :
Once I found the x = 40.
I understood that the three numbers are 120, 160, 200
I applied the formula like this :
Product of the numbers = lcm of the numbers * G.C.F of the number.
So G.C.F = product\L.C.M.
So G.C.F = (120*160*200)\2400 =1600.
Which is not the correct answer. Since the concept of G.C.F *L.C.M = product is applicable only for two numbers and not more than that.
Once I found the x = 40.
I understood that the three numbers are 120, 160, 200
I applied the formula like this :
Product of the numbers = lcm of the numbers * G.C.F of the number.
So G.C.F = product\L.C.M.
So G.C.F = (120*160*200)\2400 =1600.
Which is not the correct answer. Since the concept of G.C.F *L.C.M = product is applicable only for two numbers and not more than that.
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