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.
Divya said:
6 years ago
Why we are using lcm here instead of hcf?
(7)
Angelina said:
5 years ago
How did we get 9999? Explain it.
(4)
Subanshika said:
2 years ago
Thanks everyone for explaining the answer in detail.
(4)
Rahul said:
7 years ago
As question given greatest number then how we do LCM method ? Greatest number means HCF nah?
(3)
Mkp said:
8 years ago
Why we take LCM of these Numbers?
Why Not HCF? Can Anyone explain?
Why Not HCF? Can Anyone explain?
(2)
Prathyusha said:
6 years ago
How to identify whether the question given is based on LCM or HCF?
(2)
Tejas Kumbhar said:
1 decade ago
The Logic here is this:
We have to find the greatest 4 digit number which is divisible by 15, 25, 40 and 75, hence it is a multiple of all these.
The LCM(15, 25, 40, 75) = 600 i.e. the least common multiple.
Hence all other common multiples of 15, 25, 40 and 75 will be multiples of 600 as well.
So to find the highest 4 digit one among all the common multiples, divide all the options by 600 to check which is perfectly divisible by 600. We get 9600, which is the answer.
We have to find the greatest 4 digit number which is divisible by 15, 25, 40 and 75, hence it is a multiple of all these.
The LCM(15, 25, 40, 75) = 600 i.e. the least common multiple.
Hence all other common multiples of 15, 25, 40 and 75 will be multiples of 600 as well.
So to find the highest 4 digit one among all the common multiples, divide all the options by 600 to check which is perfectly divisible by 600. We get 9600, which is the answer.
(1)
PRAKASG said:
10 years ago
Nice explanation.
(1)
Mahima said:
10 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:
10 years ago
Please explain me if the 2 are already repeated in 25 then why you have taken for 3 times?
(1)
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