ferrarih wrote:

If 2^x*3^y*7^z is divisible by 168 and 441. What is the least value of x*y*z if we consider x, y and z integers?

A. 3

B. 4

C. 5

D. 6

E. 12

OA: EIf \(2^x*3^y*7^z\) is divisible by \(168\) i.e. \((2^3*3*7)\),then \(x\geq{3}, y\geq{1}\) and \(z\geq{1}\).

If \(2^x*3^y*7^z\) is divisible by \(441\) i.e. \((2^0*3^2*7^2)\),then \(x\geq{0}, y\geq{2}\) and \(z\geq{2}\).

So If \(2^x*3^y*7^z\) is divisible by \(168\) and \(441\), Minimum Value of \(x\) should be \(3\), \(y\) should be \(2\) and \(z\) should be \(2\).

The least value of \(x*y*z = 3*2*2 = 12\)