Question

if a=7³ *5⁴ *3⁵, b =15 *10² then gcd(a,b)=
a.375
b.150
c.75
d.90​

Answer 1

Answer:

The correct answer is option (a) .

Step-by-step explanation:

Given $a=7^3\times 5^4\times 3^5$

And    $b=15\times 10^2=3\times 5\times (2\times 5)^2=2^2\times 3\times 5^3$

Therefore

          $\text{gcd}(a,b)=3^1\times 5^3=3\times 125=375$

( Since least power of 3 among a and b is 1 and least power of 5 among a and b is 3)