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What does HCF mean?

And Xth CBSE?

Oh CBSE is some kind of exam,

oh so hcf is gcf

or also known as gcd

yes it is

i guess you've put it right

we might be able to use this
\[lcm(a,b)=\frac{| a \cdot b|}{\gcd(a,b) }\]

\[lcm(p,q)=\frac{p q}{\gcd(p,q)}=\frac{pq}{2} \\ lcm(p,r)=\frac{pr}{\gcd(p,r)}=\frac{pr}{1}=pr\]

drop the absolute value because you know p and q and r are positive so there product will be too

I guess we aren't given the gcd(q,r)

No, I've copied the question faithfully from the worksheet I received.

you know I think q might be even since gcd(p,q)=2

so I think we are actually done

anyways I know you are gone now :p

do the integers `4, 6, 3` satisfy the given conditions

was just cooking up based on prime factorization of 72..

yeah looks there is no unique answer, lcm could be either 24 or 36

I'm going to see if I can find where I went wrong with my so called logic

guess it was in assuming that q was even with the given that r was not even that gcd(q,r)=1

because like you said r=3 is not even
and q =6 is even
and gcd(6,3) is not 1

thats it i guess, you have worked the case when gcd(q, r)=1
the other case is gcd(q, r)=3

seems 4, 18, 1 also satisfy
my batery is dying brb. .

in fact \((4,6,3)\) also gives rise to \((2,12,3)\) if you redistribute your \(2\)s