SOLUTION: The LCM of two numbers is between 10 and 20.The two numbers is differ by 3.What are they?

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
RELATED QUESTIONS
if the log of two numbers are 1.7 and 2.0 by what factor do they differ? what are the two (answered by CharlesG2)

Two numbers differ by 3 and they have a quotient of 3/4. what are the... (answered by Fombitz,MathTherapy)

Two numbers differ by 3 . The sum of their reciprocal is 7/10 find the... (answered by stanbon,josmiceli)

what is the minimum product of two numbers that differ by 7? what are the... (answered by checkley77)

Two natural numbers differ by two units and the sum of thier sqaures is 580. What are... (answered by stanbon,ewatrrr)

two numbers differ by 9. the sum of their squares is 653. what are the... (answered by josgarithmetic)

two numbers differ by 18 and their sum is 68. what are the numbers (answered by mananth,checkley79)

two numbers differ by 57. the sum of the numbers is 185. What are the two... (answered by Shana-D77)

The GCF of two numbers is 18. Their LCM is 630. what are the two numbers. (answered by richwmiller)