Can two numbers have 14 as their H.C.F and 204 as their L.C.M?  

Give reasons in support of your answer. 

Let the two numbers be a and b.
∴ LCM is divisible by a and b and a and b are divisible by HCF.
∴ LCM is divisible by HCF.
Given, LCM = 204 and HCF = 14
Since 14 do not divide 204.
∴ Two numbers cannot have 14 as their HCF and 204 as their LCM.

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