Question
How many numbers from 1 to 500 (both included) are
divisible by both 4 and 6 but not divisible by 8?Solution
Numbers divisible by both 4 and 6 are divisible by LCM(4, 6) = 12 Count of multiples of 12 up to 500: = ⌊500 / 12⌋ = 41 Numbers divisible by 12 and also by 8 are divisible by LCM(12, 8) = 24 Count of multiples of 24 up to 500: = ⌊500 / 24⌋ = 20 Required numbers = 41 − 20 = 21 Answer: 21 numbers
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