Which of the following is the lowest positive integer that is divisibl

The question basically asks for the LCM of these numbers.

\(8 = 2 * 2 * 2\)

\(9 = 3 * 3\)

\(10 = 2 * 5\)

\(11 = 11\)

\(12 = 2 * 2 *3\)

LCM = \(2 * 2 * 2 *3 *3 * 5 * 11 = 3960\)

Lets start with the smallest number:

890 - Not divisible by 12 (3 * 4) as the number is not divisible by 3.
2970 - Not divisible by 8 as the last three digits are not divisible by 8
3960 - Divisible by 3, 4, 8, 9, 10 and 11.

Answer: C

No.'s are quite interesting in this case
like 2*2970 = 5940 and 2*3960=7920, this is something one should reveal himself at first look

Now looking at divisible no 8,9,10,11,12.. I will in a second try for 10, yups all no. are divisible by 10

Now for next contender i will look for a prime 11, kindly note even after dividing by 11 the no. should be divisible by 8,9,5 (out of minimum of 8, 9, 5 (10 as 2 is already considered with 8), 12 ( 4 and 3 already taken care with 8 and 9)

Starting with lowest = 890 / 11= 80 not divisible by 3
2970/11=270 not divisible by 8
3960/11= 360 divisible by 8,9,5 got it !!
5940/11 = 540 divisible by 8,9,5 but already got the answer
7920/11 = 720 already checked 3960 so it will by having, but smaller one already filtered

LCM = lowest positive integer that is divisble means the LCM of these numbers 8,9,10,11,12 = 3960

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