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. 14)
14.
The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
Answer: Option
Explanation:
L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 x 2 + 3) = 1683.
Discussion:
86 comments Page 5 of 9.
Tg said:
7 years ago
2 has come because 5*6*7*8 is 1683.
Ram said:
7 years ago
Thanks for the explanation @Suchita.
Renu said:
7 years ago
Good explanation, Thanks @Suchita.
Munna Mudassir said:
8 years ago
Another shortcut which will work in this case is checking thew divisibility by 9.
only 1683 is divisible by 9 hence the answer is 1683. In case there is more numbers divisible by you have to check it as my previous answer.
only 1683 is divisible by 9 hence the answer is 1683. In case there is more numbers divisible by you have to check it as my previous answer.
Saurabh agrawal said:
1 decade ago
Suchita's trick is great. Very short and productive.
Lali said:
1 decade ago
It clear when we put a value of k 1 then 5,6,7,8, leave the remainder 3 and 6 in case of 9. when k=2. in this case no remainder is left.
Chandresh said:
1 decade ago
But concept of finding the value of k is still not clear.
Can anyone tell the concept except logical solution?
Can anyone tell the concept except logical solution?
Satheesh said:
1 decade ago
Divide each answer by 9 which one has no reminder that's answer.
Feroz said:
1 decade ago
we get LCM =840 since 843 is divided by 3
when we divide it by 9 it leaves a remainder of 6
since we need a least no. divided by three which also leaves 3 remainder
we put value of k=1, 2, 3.... till we get the required no.
since
when we divide it by 9 it leaves a remainder of 6
since we need a least no. divided by three which also leaves 3 remainder
we put value of k=1, 2, 3.... till we get the required no.
since
Pankaj said:
1 decade ago
Nice Suchita.
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