If $$X=3^2×2, Y=2^3×3$$​ and $$Z=3^2×2^2$$​ then the L.C.M. of XY, YZ, ZX is:

Correct option is C

Given:

X = $$3^2 \times 2$$​​

Y$$= 2^3 \times 3$$​​

Z =$$3^2 \times 2^2$$​​

Required: LCM of XY, YZ, ZX

Solution:

XY $$= (3^2 \times 2) \times (2^3 \times 3) = 3^{2+1} \times 2^{1+3} = 3^3 \times 2^4$$​​

YZ $$= (2^3 \times 3) \times (3^2 \times 2^2) = 3^{1+2} \times 2^{3+2} = 3^3 \times 2^5$$​​

ZX = $$(3^2 \times 2^2) \times (3^2 \times 2) = 3^{2+2} \times 2^{2+1} = 3^4 \times 2^3$$​​

For 3: max power = 4

For 2: max power = 5

LCM of XY, YZ, ZX = ​$$3^4 \times 2^5 = 81 \times 32 = 2592$$​​