SOLUTION: What is the smallest positive integer that can be expressed as the sum of nine consecutive positive integers, the sum of ten consecutive positive integers, and the sum of eleven co

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Question 103322: What is the smallest positive integer that can be expressed as the sum of nine consecutive positive integers, the sum of ten consecutive positive integers, and the sum of eleven consecutive positive integers? Explain how you arrived at this number.
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
Before we start, let's be clear.
Positive integers are 1,2,3,4,5,.... and do not include zero. Consecutive means one right after the other (3 and 4 are consecutive integers).
What is the smallest sum from one positive integer?
1
What is the smallest sum from two consecutive positive integers?
1+2=3 Sum from 1 to 2.
What is the smallest sum from three consecutive positive integers?
1+2+3=6 Sum from 1 to 3.
There's a pattern here.
...
What is the smallest sum from ten consecutive positive integers?
The sum from 1 to 10.
1+2+3+4+5+6+7+8+9+10=55
What is the smallest sum from eleven consecutive positive integers?
The sum from 1 to 11.
Or the sum from 1 to 10 plus 11.
1+2+3+4+5+6+7+8+9+10+11=55+11=66
What is the smallest sum from twelve consecutive integers?
The sum from 1 to 12.
Or the sum from 1 to 11 plus 12.
1+2+3+4+5+6+7+8+9+10+11+12=66+12=78