A student claims that for three positive integers $p,q,r$, we always h…

Question

A student claims that for three positive integers $p,q,r$, we always have $\operatorname{HCF}(p,q,r)	imes \operatorname{LCM}(p,q,r)=p	imes q	imes r$. Which option is correct?

Accepted Answer

C. The claim is false in general for three numbers.

For two positive integers, $\operatorname{HCF}	imes \operatorname{LCM}=	ext{product of the numbers}$. But the chapter explicitly notes that this does not generally extend to three numbers. For example, for $6,72,120$, we get $\operatorname{HCF}=6$ and $\operatorname{LCM}=360$, so $6	imes 360
eq 6	imes 72	imes 120$.

Answer

The claim is always true for any three positive integers.

Answer

The claim is true only when all three numbers are prime.

Answer

The claim is true only when two of the numbers are equal.

A student claims that for three positive integers $p,q,r$, we always have $\operatorname{HCF}(p,q,r)\times \operatorname{LCM}(p,q,r)=p\times q\times r$. Which option is correct?