Question
How many numbers in the range from 300 to 900 are
divisible by 7, 14, and 28?Solution
ATQ;
If a number is a multiple of 7, 14, and 28, then the number is a multiple of the L.C.M of 7, 14, and 28.
L.C.M of 7, 14, and 28 = 28
Smallest multiple of 28 between 300 and 900 = 308
Largest multiple of 28 between 300 and 900 = 896
Common difference = 28
Let the required number of terms be 'n'.
So, 308 + (n - 1) × 28 = 896
Or, n - 1 = (896 - 308) ÷ 28 = 21
So, n = 21 + 1 = 22
So, there are 22 numbers between 300 and 900 which are multiples of 7, 14, and 28.
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