If x $$\times$$ y denotes H.C.F of x and y and x @ y denotes LCM of x and y, then the value of (72 $$\times$$ 84) @ 144 is:

If x $$\times$$ y denotes H.C.F of x and y and x @ y denotes LCM of x and y, then the is:

value of (72 $$\times$$ 84) @ 144 = LCM of [HCF of (72  and 84)] and 144    Eq.(i)

HCF of (72 and 84)

72 = $$2\times2\times2\times3\times3$$ 

84 = $$2\times2\times3\times7$$

So here 2, 2 and 3 are common. HCF of (72 and 84) = $$2\times2\times3$$ = 12    Eq.(ii)

Put Eq.(ii) in Eq.(i).

= LCM of 12 and 144    Eq.(iii)

LCM of (12 and 144)

LCM of (12 and 144) = $$2\times2\times2\times2\times3\times3$$

= 144