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 2 of 12.
Rahul said:
1 decade ago
To find the LCM use prime factorization:
15: 5 x 3
25: 5 x 5
40: 5 x 8 = 5 x 2 x 2 x 2
75: 15 x 5 = 5 x 5 x 3
LCM: Every prime factor such that none are repeated:
5 x 3 (from 15) x 5 (from 25) x 2 x 2 x 2 (from 40) and since two 5s and 3 are already there you dont take anything from 75.
so LCM is 5 x 3 x 5 x 2 x 2 x 2 = 600
Then just find the greatest 4 digit number divisible by 600. Which is shown and explained well by the problem explanation.
15: 5 x 3
25: 5 x 5
40: 5 x 8 = 5 x 2 x 2 x 2
75: 15 x 5 = 5 x 5 x 3
LCM: Every prime factor such that none are repeated:
5 x 3 (from 15) x 5 (from 25) x 2 x 2 x 2 (from 40) and since two 5s and 3 are already there you dont take anything from 75.
so LCM is 5 x 3 x 5 x 2 x 2 x 2 = 600
Then just find the greatest 4 digit number divisible by 600. Which is shown and explained well by the problem explanation.
Arunav said:
1 decade ago
There can be another approach. Just find the L.C.M. of the nos. The L.C.M. comes to be 600. Now check which is the greatest no. which is getting divided by 600.
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
In this way I guess it would be quicker than dividing 9999 and then subtracting the remainder.
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
In this way I guess it would be quicker than dividing 9999 and then subtracting the remainder.
Pratik Sakharkar said:
6 years ago
Hello.
They told that greatest 4 digits no right.
So to calculate the common multiple take lcm of 15,25,40,75.
The answer will come 600 right.
Now to check the biggest 4 digits no divide the lcm by 9000, 9400, 9600, 9800.
9000/600= 15.
9400/600=47/3 i.e 15.66 not valid.
9600/600=16.
9800/600=49/3 i.e 16.33 not valid.
So the proper 4 digits greater no is 9600 which is divided by lcm which is not in fraction, so the answer is 9600.
They told that greatest 4 digits no right.
So to calculate the common multiple take lcm of 15,25,40,75.
The answer will come 600 right.
Now to check the biggest 4 digits no divide the lcm by 9000, 9400, 9600, 9800.
9000/600= 15.
9400/600=47/3 i.e 15.66 not valid.
9600/600=16.
9800/600=49/3 i.e 16.33 not valid.
So the proper 4 digits greater no is 9600 which is divided by lcm which is not in fraction, so the answer is 9600.
(1)
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.
Neha said:
1 decade ago
Find the LCM of 15, 25, 40 and 75 which is 600.
Now, find out the multiples of 600 i.e.
600*1=600
600*2=1200
600*3=1800
........
600*16=9600
600*17=10200
We can see that the greatest number of four digits is 9600 and hence 9600 is the answer.
Now, find out the multiples of 600 i.e.
600*1=600
600*2=1200
600*3=1800
........
600*16=9600
600*17=10200
We can see that the greatest number of four digits is 9600 and hence 9600 is the answer.
Satish Kumar said:
1 decade ago
Guys don't worry. You can do this by another method.
From options 9800 is highest number so divide it with given numbers 15, 25, 40, and 75. But 75 is not divisible so forget about 9800.
Now choose the next highest number from given options that is 9600. And it is divisible by all the given numbers. That is the answer.
Don't worry about remaining options because according to the question we need the highest number.
From options 9800 is highest number so divide it with given numbers 15, 25, 40, and 75. But 75 is not divisible so forget about 9800.
Now choose the next highest number from given options that is 9600. And it is divisible by all the given numbers. That is the answer.
Don't worry about remaining options because according to the question we need the highest number.
Debashree said:
1 decade ago
Wow should we divide 9999 by 600
i) 1st we find the greatest 4 digit number
ii) Then find the lcm of 15,25,40 ,75 ,is 600 ,so 600 is least number by which 15,25,40,75.so all the multiple of 600 is divisible by 15,25,40,75
iii) Then find multiple of 600 which is less than 999
iv) So we divide 9999 by 600
and get 399 as remainder,
If substract 399 from 9999 tnen we get that number
9999 - 3999 = 9600
i) 1st we find the greatest 4 digit number
ii) Then find the lcm of 15,25,40 ,75 ,is 600 ,so 600 is least number by which 15,25,40,75.so all the multiple of 600 is divisible by 15,25,40,75
iii) Then find multiple of 600 which is less than 999
iv) So we divide 9999 by 600
and get 399 as remainder,
If substract 399 from 9999 tnen we get that number
9999 - 3999 = 9600
Suresh said:
12 months ago
When understanding the question it's clearly saying the highest 4-digit number can be divisible by 15, 25, 40 and 75.
Now see the options the Highest number is 9800. Try to divide it by 15. 9800 not divisible by 15. So 9800 is not the correct option.
Again check 9600. It can be divisible by 15, 25, 40, 75. So, 9600 is the greatest of all remaining so the answer is 9600.
Now see the options the Highest number is 9800. Try to divide it by 15. 9800 not divisible by 15. So 9800 is not the correct option.
Again check 9600. It can be divisible by 15, 25, 40, 75. So, 9600 is the greatest of all remaining so the answer is 9600.
(18)
Rattan said:
5 years ago
15 = 3*5
25 = 5*5
40 = 8*5
75 = 3*5*5
Clearly, HCF of these numbers will be 3*5*5*8.
So a number to be divisible by all four a no. must be divisible by 3, 5, and 8.
The only numbers in the options given that are divisible by these 3 are 9000 and 9600, but the question asked for the greatest no. Which means the answer is 9600.
25 = 5*5
40 = 8*5
75 = 3*5*5
Clearly, HCF of these numbers will be 3*5*5*8.
So a number to be divisible by all four a no. must be divisible by 3, 5, and 8.
The only numbers in the options given that are divisible by these 3 are 9000 and 9600, but the question asked for the greatest no. Which means the answer is 9600.
(10)
Siddharth said:
1 decade ago
Hi all,
Another method to answer this question is just break all four (15, 25, 40, 75) in to prime numbers.
15 = 5*3.
25 = 5*5.
40 = 8 (2*2*2) *5.
75 = 5*3*5.
Now here we can see the common divisors are 5, 3 and 8.
So the number which is divisible by 5, 3 and 8 is the right answer which is option C 9600.
Another method to answer this question is just break all four (15, 25, 40, 75) in to prime numbers.
15 = 5*3.
25 = 5*5.
40 = 8 (2*2*2) *5.
75 = 5*3*5.
Now here we can see the common divisors are 5, 3 and 8.
So the number which is divisible by 5, 3 and 8 is the right answer which is option C 9600.
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