Answer :

Let u = 24x^{2}yz

and v = 27x^{4}y^{2}z^{2}

Writing u and v in factorized form which is as follows:

u = 2 × 2 × 2 × 3 × x^{2} × y × z

= 2^{3} × 3 × x^{2} × y × z

v = 3 × 3 × 3 × x^{4} × y^{2} × z^{2}

= 3^{3} × x^{4} × y^{2} × z^{2}

Now selecting the common multiples from both u and v,

= 2^{3} × 3^{3} × x^{4} × y^{2} × z^{2}

= 216 x^{4}y^{2}z^{2}

Therefore the LCM of u and v = 216 x^{4}y^{2}z^{2}

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