Question

H.C.F. of 3240, 3600 and a third number is 36 and their L.C.M. is 2${}^4$ x 3${}^5$ x 5${}^2$ x 7${}^2$. The third number is ____.

• A. 2² x 3⁵ x 7²
• B. 2² x 5³ x 7²
• C. 2⁵ x 5² x 7²
• D. 2³ x 3⁵ x 7²
• E. None

Answer 1

The correct option is A

2² x 3⁵ x 7²

3240 = $2^3$ x 3${}^4$ x 5
3600 = 2${}^4$ x 3${}^2$ x 5${}^2$
H.C.F. = 36 = 2${}^2$ x 3${}^2$.
Since H.C.F. is the product of lowest powers of common factors, so the third number must have (2${}^2$ x 3${}^2$) as its factor.

Since L.C.M. is the product of highest powers of common prime factors.

So the third number must have 3${}^5$ and 7${}^2$ as its factors.

$\therefore$ Third number = 2${}^2$ x 3${}^5$ x 7${}^2$.