p, q and r are different prime numbers; a,b and c are positive whole numbers, such as abc; if n = p ^{a} q^{c} r^{b} and m = p ^{b} q^{a} r^{c}, then the greatest common divisor of m and n is :

Question

p, q and r are different prime numbers; a,b and c are positive whole numbers, such as a>b>c; if n = p ^{a} q^{c} r^{b} and m = p ^{b} q^{a} r^{c}, then the greatest common divisor of m and n is :

rock_mit182 · Answer

$$m = p ^{b} q^{a} r ^{c}$$
$$n = p^{a}q^{c}r^{b}$$

rock_mit182 · Answer

@paki @Luigi0210

rock_mit182 · Answer

@misty1212 @calculusxy plz  how do i solve this ?

rock_mit182 · Answer

@IrishBoy123

irishboy123 · Answer

to illustrate with a simpler problem

let's say you have $2^3 \ 3^5$ and $2^5 \ 3^2$

then you would go with $2^3 \ 3^2$

the lowest exponent in each case 

because 2 and 3 are prime

does that help?

irishboy123 · Answer

oh!

there are some proper mathematicians watching now

i reckon they'll do this better than me :-)

rock_mit182 · Answer

the options are:
a.$$p^{c}q^{b}c^{c}$$
b.$$p^{b}q^{b }c^{c}$$
c.
 $$p^{b}q^{c}c^{c}$$
d. $$p^{a}q^{c}c^{b}$$

misty1212 · Answer

lol
here is another hint:
since $a>b$ the greatest common divisor of $p^a,p^b$ is $p^b$ just like the greatest common divisor of $7^3$ and $7^2$ is $7^2$

misty1212 · Answer

in other words, just like with actual numbers, pick the lowest exponent

rock_mit182 · Answer

so it the answert is c because that expression has the lowest exponents ?

rock_mit182 · Answer

altought it would be a lot alike to a -.-

rock_mit182 · Answer

i guess it is C after all they have the lowest common exponents of m and n

rock_mit182 · Answer

anyway thanks to all of you :)