Question

how many three digit numbers are divisible by both 3 and 4 .
please answer this question ......​

Answer 1

Answer:

Step-by-step explanation:

LCM of 3 & 4 is 3*4 = 12 , so the smallest 3 digit number divisible by 12 is as follows :

The remainder is 4 when (100 ÷ 12). The smallest 3 digit number divisible by 12 is

(12–4) +100 =108 . The largest 3 digit number divisible by 12 is calculated as follows :

Remainder when (999÷12) is 3. Hence the largest number is 999 -3 = 996 .

** This is when divisibility results no remainder i.e the end result is whole number otherwise all the three digit numbers is divisible by 12 (3 & 4) resulting decimal numbers as quotient.

Answer 2

LCM of 3 and 4 is 12
Smallest 3 digit number is 100. When 100 is divided by12, the remainder is 4. So the smallest 3 digit number which us divisible by 3 and 4 is 100+(12-4)=108

Greatest three digit number is 999, which when divided by 12 leaves a remainder 3. So the greatest three digit number divisible by both 3 and 4 is 999-3=996

So we need to find the number of terms of the AP with first term a=108, last term an=996 and common difference d=12

So 108+(n-1)12=996
108+12n-12=996
12n=996-108+12=900
So n=75

So there are 75 three digit numbers which are divisible by 3 and 4