Question
How many numbers between 340 and 1260 are divisible by
both 18 and 24, but are not divisible by 5?Solution
If a number if multiple of 18 and 24, then it's a multiple of L.C.M of 18 and 24 = 72 Therefore, first and last multiple of 72 between 340 and 1260 are 360 and 1224, respectively Therefore, numbers are 360, 432, 504, ......, 1224 which is in arithmetic progression Therefore, first term (a) = 360, common difference (d) = 72 and nth term (an) = 1224 Therefore, an = a + (n - 1) X d Or, 1224 = 360 + (n - 1) X 72 Or, (n - 1) = (1224 - 360) ÷ 72 Or, n - 1 = 12 Or, n = 13 Now, numbers which are multiple of 72 and 5 both are 360, 720, 1080 i.e. 3 numbers Required number of multiples = 13 - 3 = 10
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