Question

How many numbers less than 500 are divisible by 2 or 3 or 4 or 5 or 7 or 21?

Answer 1

Answer:

Step-by-step explanation:

Numbers that are divisible by 3, 5 and 7 can be represented as n(3), n(5) and n(7) respectively.

Between 0 to 500,

n(3) = 500/6= 166

n(5) = 500/5 = 100

n(7)= 500/7 = 71

Total numbers = n(3) + n(5) +n(7)= 166+100+71 = 337

Here, we have calculated numbers that are divisible by 3,5 and 7 individually.

There are some numbers that have been repetitively counted, in order to eliminate them we have to find out the common numbers.

Numbers that are divisible by 3 and 5 = n(3&5) = 500/ (LCM of 3 & 5) = 500/15 = 33

Numbers that are divisible by 5 and 7 = n(5&7) = 500/ (LCM of 5 & 7) = 500/35 = 14

Numbers that are divisible by 3 and 7 = n(3&7) = 500/ (LCM of 3 & 7) = 500/21 = 23

Numbers that are divisible by 3,5 and 7 = n(3&5&7) = 500/(LCM of 3&5&7) = 500/ 105 = 4

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