108 and others such as 120,132
Method: To be divisible by 3 and 4, the desired number has to be divisible by the Least Common Multiplier or LCM of 3 and 4, that is by 12. So we have to take integral multiples of 12 and see which are the 3-digit numbers. Since 100 is the smallest 3 digit number, we have to take such multiples which would be greater than 100.
12 x 9 = 108
12 x 10 = 120
12 x 11 = 132
12 x 12 = 144
and so on.
All these numbers 108, 120, 132, 144,156……..ad infinitum are divisible by 3 and 4. Since we are asked to name ‘a 3 digit number’, we will choose 108 which is the first and the smallest of them all. Dividing 108 by 3, the quotient = 36 and remainder = 0. Dividing by 4, the quotient = 27 and the remainder = 0.
Therefore, 108 is a 3-digit number that is divisible both by 3 and by 4 (Proved)