Can two numbers have 15 as their H.C.F. and 175 as L.C.M. Give reason

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Solution

No, Two numbers cannot have HCF as 15 and LCM as 175 .
Because (i) LCM>HCF and (ii) HCF of the two numbers should divide the LCM completely.
Here , the 1st criteria is fulfilled but the 2nd criteria is not.
Since, $\frac{175}{15} = \frac{35}{3}$ (does not divide completely) ∉ N.
175 is not completely divisible by 15.

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