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. 5)
5.
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
Answer: Option
Explanation:
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600.
Discussion:
120 comments Page 3 of 12.
Lakhan said:
1 decade ago
Friends will you please explain how the LCM came 600 in detail ?
Lakhan said:
1 decade ago
@Rahul
How can you ignore 75= 15 x 5 = 5 x 5 x 3 while calculating LCM ?
How can you ignore 75= 15 x 5 = 5 x 5 x 3 while calculating LCM ?
Sam said:
1 decade ago
Great explanation Debashree.
PK rojer said:
1 decade ago
Instead of calculating LCM Why we don't go for calculating HCF.
Dr.Deepshikha Saini said:
1 decade ago
Debashree you are superb. Thanks for such a wonderful explanation.
Akshata said:
1 decade ago
@Arunav.
Your explanation seems to be quick and fast. Can you elaborate and let me know who will it work.
My funds of finding LCM in this case 600 is clear.
But when you are writing "Numbers of option B and option D are not getting divided by 600 and between option B and C (which are getting divided by 600) the number of option C is the greatest no. Divisible by 600" is not clear. Just let me know the explanation.
In this way I guess it would be quicker than dividing 9999 and then subtracting the remainder.
Your explanation seems to be quick and fast. Can you elaborate and let me know who will it work.
My funds of finding LCM in this case 600 is clear.
But when you are writing "Numbers of option B and option D are not getting divided by 600 and between option B and C (which are getting divided by 600) the number of option C is the greatest no. Divisible by 600" is not clear. Just let me know the explanation.
In this way I guess it would be quicker than dividing 9999 and then subtracting the remainder.
Aslam said:
1 decade ago
Please calculate the remainder.
Alwin said:
1 decade ago
To find LCM
15=3*5
25=5*5
40=2*2*2*5
75=3*5*5
Every number written in the form of multiples of prime number
Now we will write as
15=> 3 5
25=> - 5 5
40=> - 5 - 2 2 2
75=> 3 5 5 - - -
___________________
3 5 5 2 2 2
Then
3*5*5*2*2*2=600
Hence the result
15=3*5
25=5*5
40=2*2*2*5
75=3*5*5
Every number written in the form of multiples of prime number
Now we will write as
15=> 3 5
25=> - 5 5
40=> - 5 - 2 2 2
75=> 3 5 5 - - -
___________________
3 5 5 2 2 2
Then
3*5*5*2*2*2=600
Hence the result
Dileep Kumar M B said:
1 decade ago
How a person could know whether to take LCM or HCF? can anybody explain me when should we use these LCM and HCF ?
Rahul Vasu said:
1 decade ago
Calculating without LCM method
Shortcut way to get 600
In the option A) is given 9000 and B) 9400 and C) 9600 and D) 9800
To subtract from highest number first i.e (D-C) 9800-9600= 200 and (B-A) 9400-9000= 400
Now (D-C)=200
(B-A)=400
Add 200 + 400= 600
The questions says greatest four digit that means in every first digit is 9..so therefore there will be 4 greatest digits of 9 i.e is 9999
Hence 9999-600= 9,399
(Therefore the first digit is 9 so the rest 3 digit is 399 and hence 9999 - 399)
9999-399= 9600
Shortcut way to get 600
In the option A) is given 9000 and B) 9400 and C) 9600 and D) 9800
To subtract from highest number first i.e (D-C) 9800-9600= 200 and (B-A) 9400-9000= 400
Now (D-C)=200
(B-A)=400
Add 200 + 400= 600
The questions says greatest four digit that means in every first digit is 9..so therefore there will be 4 greatest digits of 9 i.e is 9999
Hence 9999-600= 9,399
(Therefore the first digit is 9 so the rest 3 digit is 399 and hence 9999 - 399)
9999-399= 9600
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