Bijesh wrote:
X, Y and Z are different positive integers. If \(24\)\(x^3y^3z^3\) is a square of an integer, what is the lowest common multiple of x,y and z?
Source: Gre 1 Book from jamboree
Let \(A^2 = 24x^3y^3z^3\)
\(A = \sqrt{24x^3y^3z^3}\)
\(A = \sqrt{(2)(2)(2)(3)x^3y^3z^3}\)
\(A = 2xyz \sqrt{(2)(3)xyz}\)
Notice, the product of \(xyz\) can only be 6
So, their LCM = 6
_________________
I hope this helps!
Regards:
Karun Mendiratta
Founder and Quant Trainer
Prepster Education, Delhi, Indiahttps://www.instagram.com/prepster_education/