Aptitude - Problems on H.C.F and L.C.M - Discussion

Discussion :: 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:

[A]. 74
[B]. 94
[C]. 184
[D]. 364

Answer: Option D

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.


Sonu said: (Jul 3, 2010)  
How can you find the value of k=4 i.e.
How we can divide (90k + 4)by 7.

Anonymous said: (Jul 20, 2010)  
How k=4 comes?

Mani said: (Aug 17, 2010)  
How can u choose the value of k=4 ? It can be 2 also know.

Srihari said: (Sep 17, 2010)  
It can not be 1, 2, 3 because if we substitute these numbers the result which is not divisible by 7. Let's check out. The only least number is 4.

Jpbernela said: (Oct 21, 2010)  
How can you find the value of k=4 ? conclude please.

Rahul said: (Oct 28, 2010)  
The question is a bit confusing but once you get it, it is ridiculously easy to solve. We are basically looking for a number X that has the following properties:
X/7 - no remained
x/6 - remainder of 4
X/9 - remainder of 4
X/15 - remainder of 4
X/18 - remainder of 4

Ideally, one would try and find the LCM of 6, 9, 15 and 18 but we already know the number involved is a multiple of 7 so we can quickly eliminate by dividing everything by 7. Turns out only one option remains. Check if they all divide by 6, 9, 15 and 18 to give a remainder of 4 and this is one of the easiest questions that can be asked.

Krishan Rajwar said: (Nov 27, 2010)  
Hey. Out of all the given option only 364 is the multiple of 7. Question is solved there itself.

Bhavi said: (Dec 27, 2010)  
Is there any short trick to solve these types of questions???

Jyoti said: (Jan 31, 2011)  
How the value k=4 comes?

Habibali@Mail.Com said: (Feb 11, 2011)  
Thankx Rahul...

Neetu said: (May 9, 2011)  
How k's value is 4 9k+4/7= k=4.

Please clear it.

Neetu said: (May 9, 2011)  
90k+4/7=4

How is please explain it.

Jignesh Rajput said: (May 10, 2011)  
Here, (90k+4) put each of value starting from 1,2,3,.... than after divisible by 7.when in the case of put 4th value we have not get the any remainder of (90k+4)divisible by 7..dats y take k=4.

i.e (90(1)+4)/7= remainder 3
(90(2)+4)/7= remainder 3
(90(3)+4)/7= remainder 2
(90(4)+4)/7= remainder 0
thats y take k=4.
thanks u

Sundar said: (May 26, 2011)  
Short cut method: [ Eliminating the options method ]

From this "The least multiple of 7" - we can tell the the result should be divisible by 7.

From the given 4 options, 364 is the only number divisible by 7.

Therefore, 364 is the correct answer.

Manasa said: (Jun 25, 2011)  
Thank you sundar.

Aqsa said: (Jul 3, 2011)  
@ Krishan Rajwar u made me laugh.u r good.

Sakthivel C.M said: (Jul 29, 2011)  
How did you find K ?

Anurag Nist said: (Aug 5, 2011)  
No need to find ok...

Just substitute k=1,k=2,k=3,....so on.

The question asks for least number....

The moment you get that the num is divisible by 7. stop there....

I hope u got it.

Sachin said: (Aug 21, 2011)  
Given here the answer should be multiple of 7, so simply divide all options by 7.

Then we only got the answer 364.

Koti Reddy said: (Nov 8, 2011)  
How to come k=4 ?

Sowmya said: (Nov 24, 2011)  
94 is divisible by 7 and it leaves a reminder of 4 when divided with all other given numbers so y not 94?

Meenakshi said: (Jan 12, 2012)  
@bhavi,

The trick which was said by krishna was very simple and even though you ask for a short trick ?

Akhil said: (Jan 19, 2012)  
Thank rahul.

Jennifer said: (Feb 22, 2012)  
Let required number be 90k + 4, which is multiple of 7.

How we are taking 90k+4??

Myk said: (Jun 26, 2012)  
a/b ve get quocent q and reminder r
there for a=bq+r that why 90k+4

Dipak Lal said: (Apr 8, 2013)  
L.C.M. of 6, 9, 15 and 18 is 90.

Take k =1,2,3,... till reminder is 00.

Let required number be (90 k + 4 )/7.

if k=1 then 90(1)+4/7 = 94/7 =13.42 = reminder is not 00.

if k=2 then 90(2)+4/7 = 184/7 =26.28 = reminder is not 00.

if k=3 then 90(3)+4/7 = 274/7 =39.14 = reminder is not 00.

if k=4 then 90(4)+4/7 = 364/7 =52.00 = reminder is 00.

OK now you take k = 4 because remainder 0.
Solution is 90k + 4 = 90*4 + 4 = 364.


Least value of k for which (90k + 4) is divisible by 7 is k = 4.

Required number = (90 x 4) + 4 = 364.

Anonymous said: (Jul 21, 2013)  
But in this question, the least number is 4. However, what if the number is too large. Will we have to try with every number in place of k and keep checking if it is divisible on not?

Akshara said: (Jul 27, 2013)  
So basically this is kind of a trial an error method question you just need to find the value of k such that 90k+4/7 gives 0.

Mohsin said: (Jan 9, 2014)  
How did you get 90? Can anyone please explain.

Ujwal said: (Jan 25, 2014)  
@Mohsin.

Factors of 6 = 2*3.
Factors of 9 = 3*3.
Factors of 15= 3*3*5.
Factors of 18 = 3*2*3.
LCM = 3*2*3*5= 90.

Ram said: (Jul 13, 2014)  
I'm confused to find LCM and HCF. Can anyone please explain?

Amita said: (Jul 15, 2014)  
First read the q. when we divide the all options with 6 then we get the reminder 4 in three option's 1st is 94 and 2nd 184 and 3rd is 364. when we divide the 94 and 184 with 7 we will get it is not divisible by 7, but when we divide the 364 with 7 then we get this is divisible by 7 so it will be answer.
6)74(12 6)94(15  6)364(6  6)184(3
-6 -6 -36 -18
----- ----- ------ ------
14 34 004 004
-12 -30
----- -----
02 04

After this only 364 is divisible by 7

7)364(52
-35
------
014
- 14
-------
00
-------

Another way is,
Divide all 4 option with 7. you will easily get which no. is divisible by 7.
And you will get only 364 is divisible by 7 so answer is 364.

Srishti said: (Sep 11, 2014)  
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.

Phanindra said: (Oct 26, 2014)  
Isn't it the least common multiple of 6, 7, 9, 15 and 18 with a remainder 4?

Sri said: (Jan 2, 2015)  
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.

Ananth said: (Feb 7, 2015)  
Shortest Way => Only one option divisible by 7 is "364".

Ram said: (Jun 10, 2015)  
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.

Manisha said: (Jul 17, 2015)  
Please, tell the how you calculate the value of k=4?

Sundar said: (Jul 18, 2015)  
Four different numbers are given. So take k=4 that's all.

Sravanthi said: (Jul 24, 2015)  
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.

V!Cky said: (Sep 5, 2015)  
Divide all given answer by 7 when remainder remains 0 i.e correct answer or assume k.

Take LCM i.e 90 K+4.

Hira said: (Sep 20, 2015)  
Correct answer is 94. Read question carefully.

Anukriti said: (Sep 28, 2015)  
Is it for all cases we put the value of remainder in k; e.g if 7 is remainder then we should keep the value of k = 7? Is it general or anything else?

Anita said: (Nov 17, 2015)  
6+9+15+18 = 48.
48*7 = 336.

7*4 = 28.
Then 336+28 = 364.

364/48 = 7.5833.

Answer = 7.
Remainder = 4.

Is this right?

Abhik Sheek said: (Dec 15, 2015)  
Don't go for calculation first here it is told that multiple of 7. Here is your answer.

Satya said: (Mar 11, 2016)  
How find the value of k==4?

John Saida said: (Apr 9, 2016)  
Sir, is there any shortcut method present for this type of question other then options verification?

Ritu said: (May 18, 2016)  
But why to do lcm of 6, 9, 15, 18 here?

Will somebody help me out?

O Jung Beom said: (Jun 9, 2016)  
No need to be messed up. Here we are given a clue (multiple of 7) it means the no is to be divided by 7. We got only 364 divisible with 7.

Now just make a test by dividing 364 by 6. As it leaves a remainder of 4 so 364 is the correct answer.

Snehesh said: (Jun 15, 2016)  
In the equation,

AX + B,

-> A is the LCM of all the given values.
-> B is the remainder.
-> The first number of the form: 90A+4 is 364. Hence, the ans.

Vikas said: (Aug 14, 2016)  
Hi, friends it's very simple trick.

LCM of 6, 9, 15, 18 is 90.

We can simply write the answer 90 + 4 but in question, it should be multiple of 7.

So (90k + 4) / 7 now we have to find the value of 'k' to complete the answer.

The first method is to substitute the value of k = 1, 2, 3. And divide it by 7 and sees the result. It actually time taking.

Now the trick:

(90k + 4) / 7 = 90k / 7 + 4 / 7,

The remainder of 4 / 7 is 4,

Remainder 90k / 7 is 6k.

Now add both remainders 6k+4 it should be divided by 7.

Now substitute the value of k it comes out be 4.

Put 90 * 4 + 4 = 364.

Narendra said: (Oct 21, 2016)  
Guys , here it is asked the least multiple so the answer is 94.

This will satisfy all the conditions.

Gurpreet Singh said: (Oct 27, 2016)  
I understand you trick, Thank you @Jignesh Rajput.

Priya said: (Jan 9, 2017)  
How Lcm of 90 come? Please explain.

Prince said: (Feb 8, 2017)  
@Priya it is so easy.

6 = 2 * 3
9 = 3 * 3
15 = 3 * 5
18 = 2 * 3 * 3.

Take one number from common multiple and multiply rest digits.
2*3*3*5.

Chanchal said: (Mar 22, 2017)  
90k + 4/7 find k.
90k/7 + 4/7.

We have to distribute 90 k as multiple of 7 and divisible by 7.
12 * 7k + 6k + 4/7.
12 * 7k/7 + 6k + 4/7.

Now we can put the value of k in 6k+4/7.

Ananya said: (Jun 7, 2017)  
Hey guys, what will we take in the right-hand side? Please help me out.

Shruti said: (Aug 7, 2017)  
You don't need to take anything on right-hand side. Just see whether the values of k when multiplied and added are a multiple of 7.

Bappi Sah said: (Aug 23, 2017)  
By formula;.

Given reminder is 4, and divisor is 6, 9, 15, 18 and lcm of 6, 9, 15, 18 is 90. To find dividend we have to multiply 90 with remainder 4 and then add remainder ie 4.

Sushil said: (Mar 5, 2018)  
Here is my simple explanation.

I think everyone is understanding how did they get ab = 12,
now if first no. is 13a,
and second no. is 13b,
factors of 12 can be (1,12) (3,4) (6,2),

Now, see if you include any common factor in a and b both then that will increase the H.C.F as HCF if highest common factor like if we take factor 6 and 2 then there is common factor between 6 and 2 which is 2 so HCF will change now to 26 that's why we can't take 6 and 2.
So only 2 pairs (1,12) (3,4).

Shakir said: (Mar 6, 2018)  
Here you can check from option also which is divisible of 7 like;
74 is not completely divided by 7.

Same as 94 and 184 also, But 364 is completely divisible by 7, So 364 is the answer.

Mansi said: (May 20, 2018)  
Answer = 7.
Remainder = 4,
7*4 =28.
which answer divide by 28 that is the correct answer is it right?

Sweet said: (Jun 24, 2018)  
How come 90k+ 4?

Denusan said: (Jul 14, 2018)  
When the leaves of the remainder is not equal to get the value of 4 then 90+4=94.

Is it right thew given is used in it.

Adi said: (Sep 24, 2018)  
How 90k+4 ?

Please explain this step.

Sai Kowsalya.D said: (Oct 2, 2018)  
K=4 because 4 is d Perfect no that suits to d equation i.e (90k+4).

If we substitute k=4 then it becomes 364 hence 364 is divisible by 7 i.e 52 hence k=4.

Dashi said: (Jan 12, 2019)  
Thanks for the answer @Jignesh.

Smile said: (Feb 18, 2019)  
I didn't understand this problem.

Please anyone explain this problem clearly.

Deb said: (Mar 24, 2019)  
It should be 94 which is divisible by 7 as well as leaves reminder 4 for other number.

Deepak said: (Apr 6, 2019)  
Thanks all.

Aditya Kulkarni said: (May 28, 2019)  
@All.

Here, We have been asked for a least multiple of 7, therefore one of the numbers given in option must be divided by 7.

74, 94 and 184 are not divisible by 7, but 364 is. So, 364 is the answer.

Jaisri said: (Jun 17, 2019)  
6, 9, 15, 18 LCM is 90.

Least number from this is 6. So 90+6= 96 when 96รท7 is 73 then remainder is 4.

Tushar said: (Jun 28, 2019)  
L.C.M. of 6, 9, 15 and 18 is 90.

Let the 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.

90K+4 is the required no.
How?

If K=1
90*1+4=94 , it is not multiple of 7.
90*2+4=184, it is not multiple of 7.
90*3+4=274, it is not multiple of 7.
90*4+4=364, it is multiple of 7.
So the least value will be 364.

Shalini said: (Jul 3, 2019)  
LCM of 6, 9, 15, 18 is 90.

Such that there is one formula these type of questions ie "LCM*k+remainder "should be divisible by a multiple.

So we want to do "trail and error" method by giving value from the options to the 'k' so that the number is divisible, so we substitute k=4.

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