Question
How many numbers in the range from 100 to 800 are
divisible by 8, 12, and 16?Solution
ATQ;
If a number is a multiple of 8, 12, and 16, then the number is a multiple of the L.C.M of 8, 12, and 16.
L.C.M of 8, 12, and 16 = 48
Smallest multiple of 48 between 100 and 800 = 144
Largest multiple of 48 between 100 and 800 = 768
Common difference = 48
Let the required number of terms be 'n'.
So, 144 + (n - 1) × 48 = 768
Or, n - 1 = (768 - 144) ÷ 48 = 13
So, n = 13 + 1 = 14
So, there are 14 numbers between 100 and 800 which are multiples of 8, 12, and 16.
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