Question
How many integers are there
between 50 and 600 that are divisible by both 15 and 25?Solution
ATQ, If a number is divisible by both 15 and 25, then it is divisible by the L.C.M of 15 and 25 = 75. And, the required integers will form an arithmetic progression. So, the first term (a) = 75 × 1 = 75 Common difference (d) = 75 Let the required number of terms be 'n'. We have, a+(n−1)d = 600 (since 600 is the greatest multiple of 75 within the given range). Or, 75+75(n−1) = 600 Or, 75+75n − 75 = 600 Or, 75n = 600 So, n = (600/75) = 8
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