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Write the HCF and LCM of the smallest odd composite number and the smallest odd prime number. If an odd number of p divides $q^{2}$ , then will it divide $q^{3}$ also? Explain.

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Yes

Yes, when q too divides the p

None

answer is A.

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Detailed Solution

We have taken two number
p and q are odd number
We know,
Smallest odd prime number =3
Smallest odd composite number = 9
Highest common factor of HCF (3, 9) = 3
Lowest common factor LCM (3, 9) = 9
When we consider odd number

p

is divided by

q^{2}

Thus,

p

is a factor of

q^{2}

Now,

q^{2} \times q = q^{3}

q^{2} \times q

[it will be factor of

q^{3}

]
Then,

p

is a factor of

q^{3}

Therefore, p is divided by

q^{3}

Correct option is 1.

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