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. 10)
10.
The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:
Answer: Option
Explanation:
L.C.M. of 6, 9, 15 and 18 is 90.
Let required number be 90k + 4, which is multiple of 7.
Least value of k for which (90k + 4) is divisible by 7 is k = 4.
Required number = (90 x 4) + 4 = 364.
Discussion:
89 comments Page 8 of 9.
Hira said:
1 decade ago
Correct answer is 94. Read question carefully.
V!cky said:
1 decade ago
Divide all given answer by 7 when remainder remains 0 i.e correct answer or assume k.
Take LCM i.e 90 K+4.
Take LCM i.e 90 K+4.
Sravanthi said:
1 decade ago
It is given in the question that it should be least multiple of 7 which leaves remainder 4. So why don't it be 94. Please clarify.
Sundar said:
1 decade ago
Four different numbers are given. So take k=4 that's all.
Manisha said:
1 decade ago
Please, tell the how you calculate the value of k=4?
Ram said:
1 decade ago
k=4 because we need least value of k which is divided 7.
So in equation 90k+4. If k=4 then answer is 364 which is divisible by 7.
So in equation 90k+4. If k=4 then answer is 364 which is divisible by 7.
Ananth said:
1 decade ago
Shortest Way => Only one option divisible by 7 is "364".
SRI said:
1 decade ago
You will have 90k+4.
Now we know 90/7 gives - 12.85 so, we can write 90 as 84k+6k.
So 90k+4 can be written as (84k)+6k+4. The first part 84k is divisible by 7. So no need to check. The second part i.e. 6k+4 has to be divisible by 7.
K = 1, 6(1)+4 = 10 X.
K = 2, 6(2)+4 = 16 X.
K = 3, 6(3)+4 = 22 X.
K = 4, 6(4)+4 = 28.
So this is divisible by 7 hence your answer is 84(4)+6(4)+4.
Hope this clarifies.
Now we know 90/7 gives - 12.85 so, we can write 90 as 84k+6k.
So 90k+4 can be written as (84k)+6k+4. The first part 84k is divisible by 7. So no need to check. The second part i.e. 6k+4 has to be divisible by 7.
K = 1, 6(1)+4 = 10 X.
K = 2, 6(2)+4 = 16 X.
K = 3, 6(3)+4 = 22 X.
K = 4, 6(4)+4 = 28.
So this is divisible by 7 hence your answer is 84(4)+6(4)+4.
Hope this clarifies.
Sonu said:
2 decades ago
How can you find the value of k=4 i.e.
How we can divide (90k + 4)by 7.
How we can divide (90k + 4)by 7.
Srishti said:
1 decade ago
Here is a simple logic.
First find the LCM of the no.s which comes 90.
Now find the no. among the options greater than 90 and divisible by 7.
First find the LCM of the no.s which comes 90.
Now find the no. among the options greater than 90 and divisible by 7.
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