Write the hcf and lcm of smallest odd composite
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write the HCF and LCM of smallest odd prime number and smallest odd composite number. If odd number p divides q 2 then will it divide q 3 also? Explain
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Solution:-
Smallest odd prime number = 3
Smallest odd composite number = 9
H.C.F. of (3, 9) = 3
L.C.M. of (3, 9) = 9
As odd number p divides q².
⇒ p is a factor of q² or q²/p gives 0 as a remainder.
Now,
q² × q = q³, and p is a factor of q², hence it will also be a factor of q² × q.
⇒ p is a factor of q³
Therefore, p will divide q³ also.
In general, we can say that if p divides q² then it will also divide qⁿ, where n is a natural number (n ≥ 2).
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