Question

write hcf & lcm of the smallest odd composite number and the small odd prime no. if an odd no. p provide q square then will it divide qcube also?.​

Answer 1

Answer:

3

Step-by-step explanation:

(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 :-)

Answer 2

Step-by-step explanation:

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