Question
How many numbers in the range from 50 to 500 are divisible
by 3, 6, and 9?Solution
ATQ;
If a number is a multiple of 3, 6, and 9, then the number is a multiple of the L.C.M of 3, 6, and 9.
L.C.M of 3, 6, and 9 = 18
Smallest multiple of 18 between 50 and 500 = 54
Largest multiple of 18 between 50 and 500 = 486
Common difference = 18
Let the required number of terms be 'n'.
So, 54 + (n - 1) × 18 = 486
Or, n - 1 = (486 - 54) ÷ 18 = 24
So, n = 24 + 1 = 25
So, there are 25 numbers between 50 and 500 which are multiples of 3, 6, and 9.
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