If X is divisible by 2,6,9,12,15,30, is X divisible by 8?

Question

The easiest method to arriving at an answer?

Vips0000 · Answer

Findout factors and derive unique combination of it. But that should be done only for very complicated numbers. For small numbers u can just observe:

For the given question.. we have 8 => 2^3
None of the given choices can give u a multiple of 2^3. So ans is No.

To find out how to use it, If the question has asked 18 then? factors, 18 = 2 * 3^3
We have 2 which gives 2^1 and 9 which gives 3^3. Hence Ans would have been Yes.

ambitiousgal · Answer

I didnt get the point

We can see a multiple of 8 too! 12 = 4 X 3 2 is already there. so we do have 2^3 right?

Vips0000 · Answer

No.. 
12 = 2^2 * 3^1 
2 = 2^1
in both 2 and 12 there is one common 2. 
When u need to find out if a number A is divisible by number B, you need to be able to ascertain that all the factors of B are in A. 
So if a number X is divisible by 12 and 2, you know that X has atleast 2^2 and 3^1 (For it to be divisible) it can guarantee that X will be divisible by 2, 4, 6, 12. Beyond this, this information can not give anything else.
eg. consider that X =12. It is divisible by 12 and 2 but not by 8.

PareshGmat · Answer

I'll say NO.
Take for ex 180. It is divisible by all 2,6,9,12,15,30.......... but not divisible by 8.
So, as 2,6,9,12,15,30 does not have a multiple of 8, there LCM is not divisible by 8

KarishmaB · Answer

Technically, it is incorrect to say 'No'.
The answer to the question is 'Cannot say/May be'

Looking at the factors, we do not see any which has an 8 in it so we cannot say that X must have 8 as a factor. 
But, there is nothing to say that it is not divisible by 8 in addition to all the factors given above.

i.e. X can be 180 (as you pointed out) and X can also be 360 (in which case it is divisible by 8)

nhattruong1302 · Answer

If X is divisible by 2,6,9,12,15,30, is X divisible by 8?

.
the answer is
.
2=2
6=3*2
9=3*3
12=3*2*2
15=3*5
30=2*3*5

The least possible value of X is X=2*2*3*3*5 (Not divisible by 8).
However, a greater value of X could be X=2*2*2*3*3*5 (divisible by 8)

If X is divisible by 2,6,9,12,15,30, is X divisible by 8?

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