Let a and b be two positive integers such that , where p and q are prime numbers. If and then

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
Let a and b be two positive integers such that $a = p^{3} q^{4} and b = p^{2} q^{3}$ , where p and q are prime numbers. If $HCF (a, b) = p^{m} q^{n}$ and $LCM (a, b) = p^{r} q^{s},$ then $(m + n) (r + s) =$

1 15

2 30

3 35

4 72

Ans.
(3)

$a = p^{3} q^{4} and b = p^{2} q^{3}$

$HCF (a, b) = p^{2} q^{3}$ ...(i)

and $LCM (a, b) = p^{3} q^{4}$ ...(ii)

But gives: $HCF (a, b) = p^{m} q^{n}$ and $LCM (a, b) = p^{r} q^{s}$

From eq. (i), $p^{m} q^{n} = p^{2} q^{3}$

So, $m = 2$ and $n = 3$

From eq. (ii), $p^{r} q^{s} = p^{3} q^{4}$

So, $r = 3$ and $s = 4$

$∴$ $(m + n) (r + s) = (2 + 3) (3 + 4) = 35 .$

Want Us to Email you About Special Offers & Updates?