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 8 of 12.
Pravin said:
9 years ago
5) 15,25,40,75
------------
5) 3,5,8,15
------------
3) 3,1,8,3
------------
1,1,8,1
Now,
LCM = 5 * 5 * 3 * 8 = 600
LCM = 600.
600)9999(16
-------------
600
3999
3600
399 --> reminder.
9999 - 399 = 9600 answer.
------------
5) 3,5,8,15
------------
3) 3,1,8,3
------------
1,1,8,1
Now,
LCM = 5 * 5 * 3 * 8 = 600
LCM = 600.
600)9999(16
-------------
600
3999
3600
399 --> reminder.
9999 - 399 = 9600 answer.
Atul said:
9 years ago
@Pravin.
I agree with you. Thank you.
I agree with you. Thank you.
Kanwar Jackson said:
9 years ago
399 is subtracted so that the number may be exactly divided.
To understand this, take an example.
If we divide 20 by 3, the remainder is 2. So 20 is not divisible by 3 but if I subtract remainder from it i.e. 20 - 2 = 18, now it will be exactly divisible by 3. (ie) 18/3 = 6.
Hope this helps!
To understand this, take an example.
If we divide 20 by 3, the remainder is 2. So 20 is not divisible by 3 but if I subtract remainder from it i.e. 20 - 2 = 18, now it will be exactly divisible by 3. (ie) 18/3 = 6.
Hope this helps!
PRAKASG said:
9 years ago
Nice explanation.
(1)
Mahima said:
9 years ago
Find the greatest 3-digit number which is exactly divisible by 4,8 and 12?
Anyone solve this?
Anyone solve this?
(1)
Tina said:
9 years ago
Please explain me if the 2 are already repeated in 25 then why you have taken for 3 times?
(1)
Arun said:
9 years ago
Guys, In question, they ask 15, 25, 40 & 75 is divisible by the greatest number of four digits.
So they give 4 digits means.
9999 is the big digit, okey leave this one .
Given options a)9000 b) 9400 c)9600 d)9800.
First we take L.C.M of 15, 25, 40 & 75 = 600.
In options first big one is 9800 so divide with 600 (9800/600=is not divisible).
So take second big one is 9600 so divide with 600(9600/600=is divisible with 16).
Third big one is 9400 so divide with 600(9400/600 = is not divisible).
Fourth big one is 9000 so divide with 600(9000/600 = is divisible with 15).
Then what's the question is the biggest 4 digit number is divisible with 15,25,40&75.
Here given options two 4 digit's number is divisible (i.e.9000, 9600).
In question ask the greatest 4 digit number (9000 & 9600 which is big one) And obviously answer is 9600.
So they give 4 digits means.
9999 is the big digit, okey leave this one .
Given options a)9000 b) 9400 c)9600 d)9800.
First we take L.C.M of 15, 25, 40 & 75 = 600.
In options first big one is 9800 so divide with 600 (9800/600=is not divisible).
So take second big one is 9600 so divide with 600(9600/600=is divisible with 16).
Third big one is 9400 so divide with 600(9400/600 = is not divisible).
Fourth big one is 9000 so divide with 600(9000/600 = is divisible with 15).
Then what's the question is the biggest 4 digit number is divisible with 15,25,40&75.
Here given options two 4 digit's number is divisible (i.e.9000, 9600).
In question ask the greatest 4 digit number (9000 & 9600 which is big one) And obviously answer is 9600.
Nagalakshmi said:
9 years ago
Why we should take LCM of number instead of taking HCF? Anyone can explain clearly?
Nithi said:
9 years ago
If you do 'daa' method to get the LCM for 15, 25, 40, 75 as 5, 5, 3, 8. Then to multiply 5 * 5 * 3 * 8 = 600.
5 | 15, 25, 40, 75
|___________________
5 | 3, 5, 8, 15
|___________________
3 | 3, 1, 8, 3
|_____________________
8 | 1, 1, 8, 1
|_______________________
===> 1, 1, 1, 1
Therefore, 5 * 5 * 3 *8 = 600.
5 | 15, 25, 40, 75
|___________________
5 | 3, 5, 8, 15
|___________________
3 | 3, 1, 8, 3
|_____________________
8 | 1, 1, 8, 1
|_______________________
===> 1, 1, 1, 1
Therefore, 5 * 5 * 3 *8 = 600.
Rasika shelke said:
9 years ago
Greatest 4 digit number = 9999.
LCM = 15, 25, 40, 75.
15 = 5 * 3.
20 = 5 * 5.
40 = 5 * 2 * 2 * 2.
75 = 5 * 5 * 3.
Then the lcm is => 5 * 5 * 2 * 2 * 2 * 3 = 600.
So, divide greatest number by 600.
9999/600 = 399.
Required number = (9999 - 399) = 9600.
So option "c".
LCM = 15, 25, 40, 75.
15 = 5 * 3.
20 = 5 * 5.
40 = 5 * 2 * 2 * 2.
75 = 5 * 5 * 3.
Then the lcm is => 5 * 5 * 2 * 2 * 2 * 3 = 600.
So, divide greatest number by 600.
9999/600 = 399.
Required number = (9999 - 399) = 9600.
So option "c".
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