3. How many positive integers less than 100 are multiples of both 4 and 6?
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To find all of the positive integers less than 100 that are multiples of both 4 and 6, begin by finding the least common multiple of 4 and 6.
Try out the multiples of 6 on 4:
6 is not a multiple of 4.
12 = 4 × 3
So in fact we want all the positive integers less than 100 that are multiples of 12. You could either estimate by dividing 100 by 12, or you could simply list them out:
12
24
36
48
60
72
84
96
Thus there are a total of 8.
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