1
$\begingroup$

There exist a formula to easily find the least common multiple of 2 integers:

$$ \operatorname{lcm}(x,y)=\frac {x\cdot y}{\gcd(x,y)} $$

And for multiple numbers:

$$ \operatorname{lcm}(a_1, a_2, \ldots ,a_n)=\frac {a_1\cdots a_n}{\gcd(a_1, a_2, \ldots ,a_n)} $$

I need help proving the latter by induction relying on the former formula.

$\endgroup$
7
  • $\begingroup$ Don't exist the gdc of >2 numbers $\endgroup$ Dec 15, 2015 at 8:04
  • 3
    $\begingroup$ @vvnitram Sure it exists. But the formula in the question is certainly wrong. $\endgroup$
    – Erick Wong
    Dec 15, 2015 at 8:05
  • $\begingroup$ Counterexample lcm(5,2,4)=20 and "gdc" is 1 $\endgroup$ Dec 15, 2015 at 8:06
  • $\begingroup$ @ErickWong no, is two to two $\endgroup$ Dec 15, 2015 at 8:07
  • 1
    $\begingroup$ @vvnitram Are you confusing "exist" with "equals"? What do you mean by "is two to two"?? $\endgroup$
    – Erick Wong
    Dec 15, 2015 at 8:08

0

You must log in to answer this question.

Browse other questions tagged .