EMNA Q.11

11HCF and LCM of two numbers is given. It is possible to find out the two numbers uniquely if
I. either sum or difference between the two numbers is known.
II. HCF of two numbers = LCM of two numbers.
III. (LCM/HCF)= Prime number.

Option : D
Explanation : Let HCF be h and LCM be l.
I. Let, numbers be ah and bh. Then abh = and (a + b)h = m
=> (a — b)h = n
Using these ah and bh can be uniquely determined. Thus, I is true II.
II. If HCF = LCM, then two numbers are equal and same as HCF or LCM. Thus, II is true.
III. LCM/HCF = prime i.e. l/h =P Then one of the numbers is equal to h and other is equal to E. Thus, III is true.

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