Question 285529: How many positive integers below 2009 are divisible by both 4 and 6?
A. 502 B. 334 C. 167 D. 83 E. None of these.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 4 goes into 2009 502.2 times.
6 goes into 2009 334.833333 times.
The least common multiple of 4 and 6 appears to be 12.
This is because 3*4 = 12 and 2*6 = 12.
12 goes into 2009 167.4166667 times.
Round that down to the nearest integer and you get 167.
I believe that's your answer.
In between those numbers, 4 and 6 do not both divide into the numbers.
If you go up by 4 from 1 to 48, you get:
4,8,12,16,20,24,28,32,36,40,44,48
If you go up by 6 from 1 to 48, you get:
6,12,18,24,30,36,42,48
The common numbers are:
12,24,36,48
These are the numbers that are divisible by both 4 and 6.
Notice they are all multiples of 12.
Your answer is selection C (167).
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