What is the smallest positive 3 digit number that leaves a remainder of 2 when divided by 3, 4, 5 or 6?
John, Brilliant_org is supposed to be a community of learners. If we give you the answer to solve something like this, then we are defeating the purpose of learning.
I solved this problem, you can either do it by obtaining it through the lowest common multiple, or the say I did it.
If you are familiar with computer programing, you can creat a for loop that loops and integer x from 100 to 1000. You can then implement if statements as conditions to which remainders of numbers are printed
i.e. if (x % 3 == 2)
_ if (x % 4 == 2)
_ if (x % 5 == 2)
_ if (x % 6 == 2)
If you do this you can print each number for each of these factors and see which one meets up first in your list of numbers as a result.
If you need help I would also read the techniques on Brilliant so that you can become stronger in the areas where you feel stumped such as this one.
Best of Luck ;)
I think someone answered your question.
To find the smallest positive 3-digit number that leaves a remainder of 2 when divided by 3, 4, 5, or 6, we can use the concept of the least common multiple (LCM) and the method of checking multiples.
Step 1: Find the least common multiple (LCM) of the divisors 3, 4, 5, and 6.
The LCM of 3, 4, 5, and 6 is the smallest positive number that is divisible by all of these numbers. To find the LCM, we can list the multiples of each number until we find a common multiple.
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Multiples of 6: 6, 12, 18, 24, 30, ...
Looking at the multiples, we see that the least common multiple of 3, 4, 5, and 6 is 12.
Step 2: Find the smallest positive 3-digit number that leaves a remainder of 2 when divided by 12.
To find this number, we can start with 102 (the smallest 3-digit number) and check each number until we find one that leaves a remainder of 2 when divided by 12.
102 divided by 12 = 8 remainder 6
103 divided by 12 = 8 remainder 7
104 divided by 12 = 8 remainder 8
105 divided by 12 = 8 remainder 9 (This is the smallest positive 3-digit number that leaves a remainder of 2 when divided by 12)
Therefore, the smallest positive 3-digit number that leaves a remainder of 2 when divided by 3, 4, 5, or 6 is 105.