We know the 3 numbers have to be a multiple of 2, 3 , 4 respectively. We know that we have to find every pattern and all of the patterns can’t have a remainder. Therefore, we have to find the LCM because it can find every number without missing a single one.
First we have to find the LCM, (Lowest Common Multiple) of 2,3 and 4, which is 12. The reason that we found the LCM is because the first number that is a multiple of 2,3 and 4 is 0, and to understand the next number that is a multiple of 2, 3 and 4.
We can continue finding the numbers which satisfy these conditions, ( are divisible by 2,3 and 4). We can find the numbers, because as we did with 0 (The base number), we add 2 for the multiple of 2, add 3 for the multiple of 3 and add four for the multiple of 4.
To ensure that this strategy works, we can do 12 + 2, 12 + 3, 12 + 4 so we get the answer 14, 15, 16 and 14 being divisible by 2 and 15 being divisible by 3 and 16 being divisible by 4.
Therefore, we can say that this strategy works for this solution. To be extra sure, we can try the next common multiple,which is 24.