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# Can two numbers have $15$ as their HCF and $175$ as their LCM? Give reasons.

**Given:**Two numbers.

**To do:**To find weather two numbers have $15$ as their HCF and $175$ as their LCM. and to explain reasons.

**Solution:**

For 2 or more numbers,

LCM$=$Product of highest power of each factor involved in the numbers.

HCF$=$Product of smallest power of each common factor.

We can conclude that LCM is always a multiple of HCF, i.e.,

LCM$=$ k$\times$ HCF

We are given that

LCM $= 175$

HCF $= 15$

But in this case, LCM $\

eq k\times$ HCF.

eq k\times$ HCF.

Therefore, 2 numbers can't have LCM as $175$ and HCF as $15$.

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