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.
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)
Ram said:
2 decades ago
How to find the l.c.m number the value is 600?
Thom said:
2 decades ago
How to find 600 is LCM?
Nitya said:
1 decade ago
Just find the lcm of 15, 40, 25, 75.
Then you will get the answer as 600.
Then you will get the answer as 600.
Darshana said:
1 decade ago
How to find the l.c.m number the value is 600?
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.
Pavan said:
1 decade ago
Why subtracted 9999-399?
Vishnu said:
1 decade ago
Just check if the answers are divisible by 40(one of the numbers given)...It's easy to notice that 9000,9400 and 9800 will not be divisible. So, it's obviously 9600.
Aparna said:
1 decade ago
@vishnu.
How 9000, 9400 and 9800 are not divsible by 40?.
It is divisible by 40.
How 9000, 9400 and 9800 are not divsible by 40?.
It is divisible by 40.
Gwene said:
1 decade ago
Vishnu why should we divide by 40?
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