Question

How many numbers in the range from 100 to 800 are divisible by 8, 12, and 16?

Q: Answer-&lt;p&gt;How many numbers in the range from 100 to 800 are divisible by 8, 12, and 16?&lt;/p&gt;

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 times 48 768 Or, n - 1 768 - 144 divide 48 13 So, n 13 1 14 So, there are 14 numbers between 100 and 800 which are multiples of 8, 12, and 16.