SOLUTION: i am a factor of 120, and a common multiple of 3, 4, and 10. The sum of my digits is 6.

Question 611475: i am a factor of 120, and a common multiple of 3, 4, and 10. The sum of my digits is 6.
Answer by KMST(5330) (Show Source): You can put this solution on YOUR website!

So, the prime factorization of 120 is

while and
A multiple of 4 needs to have in its factorization.
A multiple of 10 needs to have in its factorization.
A multiple of 3 needs to have in its factorization.
The number is the smallest number that has all the factors needed, and is the answer to the problem.

so it is a multiple of 10.
so it is a multiple of 3.
so it is a multiple of 4.

We could include more factors, but that would result in larger numbers, and most of them would be larger than 120, so they would not be factors of 120, and would not be a solution to the problem.
Adding factors, the smallest number we could get is when we include the smallest factor (another 2) as an extra factor. Then we get the only other factor of 120 that is also a common multiple of 3, 4, and 10.
, is a multiple of 120, but its digits do not add to 6.
RELATED QUESTIONS
I am less then 90, I am a multiple of 5, and the sum of my digits is 9 (answered by josmiceli)

i am a multiple of both 3 and 7 the differnce between my two digits is 3 what am i... (answered by ankor@dixie-net.com)

i have 3 digits, i am a palindrome, i am a multiple of 2. the product of my digits is... (answered by Grinnell)

my number has 2 digits,and both digits are even the sum of my numbers digits are 10 my... (answered by mananth)

I am a number between 6 and 150. I am one more than a square number. The sum of my... (answered by Edwin McCravy)

I am a 3 digit number. I am a multiple of 50. My first 2 digits are even and their... (answered by richard1234)

What is my number? I am a multiple of 6 but less than 50 I am an even number The sum... (answered by rothauserc)

I'm a Common multiples of 4 & 6 and sum of my digit is 6, which number am... (answered by karan037)

I am a multiple of 5. The sum of my 2 digits is 8. What am... (answered by ikleyn)