The number of common roots of the 15th and  of 25th roots of unity are
• A
1
• A
1
• B
5
• B
5
• C
6
• C
6
• D
10
• D
10

#### Solution

$15th$ roots of unity are $e^{\dfrac{{i}2{k}\pi}{15}}$ where $k=1,2,\cdots,15$
$25th$ roots of unity are $e^{\dfrac{{i}2{m}\pi}{25}}$ where $m=1,2,3,\cdots,25$
The common roots are $e^{i\dfrac{2{n}}{5}}$ where $n=1,2,3,4,5$
Number of common roots will be $5$