How many numbers between 340 and 1260 are divisible by

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 n^th 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