Simple inequality

If l,m,n are positive integers greater than 1, lm=21 & mn=39, then which of the following must be true?
(n>l>m) or (m>n>l) or (n>m>l)?

My method: I have understood how n>l. So, I have given only those options which have (n>l). How to say anything about m?

1 Answers

62
Lokesh Verma ·

If l,m,n are positive integers greater than 1, lm=21 & mn=39, then which of the following must be true?
(n>l>m) or (m>n>l) or (n>m>l)?

My method: I have understood how n>l. So, I have given only those options which have (n>l). How to say anything about m?

n/l = 13/7

so you know that n has to be a multiple of 13

so n has to be 13 or 39 (why?)

in each case you can find m as either 1 or 3

hence you have solved it :)

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