Question
How many whole numbers between 100 and 750 are multiples
of both 18 and 24?Solution
If a number is divisible by both 18 and 24, then it is divisible by L.C.M of 18 and 24 = 72 And, the required numbers will form an arithmetic progression So, First term (a) = 72 X 2 = 144 Common difference (d) = 72 Let required number of terms be 'n' We have, a + (n - 1)d = 720 (since 720 is the greatest multiple of 72 within the given range.) Or, 144 + 72(n - 1) = 720 Or, 144 + 72n - 72 = 720 Or, 72n = 648 So, n = (648/72) = 9
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