Problem Solving

what is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?
A. 420
B 840
C, 1260
D. 2520
E. 5040

is the answer A?

One way of solving this is to work through the answer choices applying the divisibility rules.

Starting from A (420) ... since this is the lowest number in the list.

This is div by 1.
This is div by 2 (its an even number)
This is div by 3 (4+2+0 = 6 ... 6 is div by 3 ... so 420 is div by 3)
This is div by 4 (420 can be divided by 2, twice: 420/2=210 ... 210/2=105)
This is div by 5 (since units digit is a 0)
This is div by 6 (we already know this is div by 2 and 3, so its also div by 6)
This is div by 7 (420/7 = 60)

So answer is A.
Can you please let us know the Official Answer ... and where this question comes from.

Thanks.
II

Yea, II is right, using the divisibilty rules, 420 is correct. All of these numbers are divisible by 1-7, but the catch is that the question is asking for the LOWEST positive integer.

Thank you all.
OA is A.
PS 33 from OG 11th.
I have no idea about lowest positive integer. Could you pls explain more?

The answer is definitely A for sure.

this is another approach ..

1=1^1 , 2=2^1 , 3=3^1 , 4= 2^2 , 5=5^1 , 6= 2^1* 3^1 7= 7^1


LCM =1^1 * 2^2 * 3^1 * 5^1 * 7^1= 420

maria wrote:Thank you all.
OA is A.
PS 33 from OG 11th.
I have no idea about lowest positive integer. Could you pls explain more?

Hey Maria,

All you need to do is see which answers are divisible by
1, 2, 3, 4, 5, 6 and 7.

420 is divisible by all the above numbers.
For ex 420 div 2 is an integer.
If you get a fraction, then it is not one of the possible answers.


Since its the lowest
number, you do not need to look for another lower number as the answer.

Cheers,
Clinton

A trickier question, would be which number is the highest that is divisbile by all 7 numbers.


We all need to check A. 420

and every other option is a multiple of 420.

So E would be the answer!