Write the HCF and LCM of the smallest odd composite number and the smallest odd prime number. If an odd number p divides q^2 , then will it divide q^3 , also ? Explain.
Answers
(i) Smallest odd prime number
Prime number is a number with exactly 2 factors .
Smallest prime number is 2
However , smallest odd prime number is 3.
(ii) Smallest odd composite number
Composite number has more than 2 factors.
Smallest composite number is 4
However , smallest odd composite number is 9.
(iii) L.C.M and H.C.F
L.C.M of 3 and 9 is :
3 = 3 × 1
9 = 3 × 3
L.C.M = 3 × 3
= 9
L.C.M = 9
H.C.F of 3 and 9 :
3 = 3 × 1
9 = 3 × 3
H.C.F = 3
(iv) Proof :
Given :
p is an odd number that divides q²
p | q²
This means that q² / p is an integer say k
==> q² / p = k [ integer ]
Multiply both sides by q :
==> q³ / p = k q
Now k q has to be an integer .
Hence q³ is divided by p [ Proved ]
Hope it helps :-)
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Answer:
LCM=3
HCF=9
Step-by-step explanation:
Thank you.
