perplexus.info :: Just Math : Divisibility with lcm and gcd

Divisibility with lcm and gcd (Posted on 2016-08-15)

Each of X and Y is a positive integer such that:
lcm(X,Y) + gcd(X,Y) = X+Y

Is one of X and Y always divisible by the other?

Provide adequate reasoning for your answer.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

If the given equation is valid, then one of X and Y will always be divisible by the other.
For an explanation, refer to the analytic solution submitted by Paul in this location..

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re(2): Answer and reasoning	Paul	2016-08-16 11:32:42
re: Answer and reasoning	Ady TZIDON	2016-08-16 00:31:58
re: Answer and reasoning	Steve Herman	2016-08-15 16:48:43
Answer and reasoning	Paul	2016-08-15 13:30:32

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