Question 1102079: The LCM of two numbers is between 10 and 20.The two numbers is differ by 3.What are they?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
I'm not sure if there is a practical algebraic method for solving this problem that could be applied to more difficult similar problems....
We could find the answer by logical analysis...
(1) Two numbers that differ by 3 and have an LCM between 10 and 20 must both be single digit numbers.
(2) If two single digit numbers have an LCM between 10 and 20 (i.e., greater than either of the two numbers), then the larger number can't be a multiple of the first; if it were, then the LCM would be the larger of the two numbers.
So the two single digit numbers have to be different multiples of some single digit number. The only two such numbers are 2*3=6 and 3*3=9.
But by far the easiest way to solve this problem is to look at all the pairs of single digit numbers that differ by 3 and find the pair for which the LCM is between 10 and 20:
1 and 4: LCM 4
2 and 5: LCM 10 (not "between 10 and 20")
3 and 6: LCM 6
4 and 7: LCM 28
5 and 8: LCM 40
6 and 9: LCM 18
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