# 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 90*k* + 4, which is multiple of 7.

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

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

Discussion:

86 comments Page 1 of 9.
Sonu said:
1 decade 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.

Anonymous said:
1 decade ago

How k=4 comes?

Mani said:
1 decade ago

How can u choose the value of k=4 ? It can be 2 also know.

Srihari said:
1 decade ago

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:
1 decade ago

How can you find the value of k=4 ? conclude please.

Rahul said:
1 decade ago

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.

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:
1 decade ago

Hey. Out of all the given option only 364 is the multiple of 7. Question is solved there itself.

Bhavi said:
1 decade ago

Is there any short trick to solve these types of questions???

Jyoti said:
1 decade ago

How the value k=4 comes?

Habibali@mail.com said:
1 decade ago

Thankx Rahul...

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