SOLUTION: The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14. find the larger of the two numbers.

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Question 1161633: The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14. find the larger of the two numbers.
Found 3 solutions by KMST, Edwin McCravy, ikleyn:
Answer by KMST(5328) About Me  (Show Source):
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14%2A23=highlight%28322%29 ,
assuming that by "the other two factors" they mean the factors of each of the two numbers that are factors in the LCM, along with 23,
the two numbers are
322=14%2A23=2%2A7%2A23 and 13%2A23=299
Their LCM is 2%2A7%2A13%2A23=14%2A13%2A23=4186

It would be a more interesting problem if they told you that the LCM of 2 numbers is
4186=2%2A7%2A13%2A23 and they asked you
what is the largest number that could be one of the two numbers if the HCF is 23.

Answer by Edwin McCravy(20054) About Me  (Show Source):
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The HCF of two numbers is 23 and the other two factors of their LCM are 13 and
14. find the larger of the two numbers.
One must be 23∙13=299 and the other must be 23∙14=322

Their HCF is 23 and the LCM = 23∙13∙14 = 4186

The larger of the two numbers is 322.

Edwin

Answer by ikleyn(52769) About Me  (Show Source):
You can put this solution on YOUR website!
. 

    Definition of Highest Common Factor HCF.

        The Highest Common Factor HCF of two or more numbers is the highest number that divides the numbers exactly.


         // Same as the GCD (= Greatest Common Divisor)


As the problem is worded,  posted and presented,  it  ADMITS  MORE  than  ONE  solution;
if to be  PRECISELY  correct,  it admits exactly  TWO  solutions. 

One       solution is  x = 23*13*14, y = 23;  the larger number is 23*13*14 = 4186.


The other solution is  x = 23*13, y = 23*14;  the larger number is  23*14 = 322.