Question

If $132300=2^2\times 3^3\times 5^2\times a^b,$ then which of the following is true ?

• A. $a=b$
• B. $a=2b$
• C. LCM of $a$ and $b$ is 14.
• D. $a+b=8$

Answer 1

The correct option is C

LCM of $a$ and $b$ is 14.

$132300=2^2\times 3^3\times 5^2\times a^b$
By fundamental theorem of arithmetic, 132300 can be written as $2^2\times 3^3\times 5^2\times 7^2.$
On comparison, we get $a=7$ and $b=2.$
LCM of 7 and 2 is 14.