Question

Q. Can 2 numbers have 18 as their HCF and 380 as their LCM?
Please help it's urgent
Ch - Real Numbers
Class 10th
Don't even try to post irrevalent answers otherwise your 10 answers will be reported​

Answer 1

$\huge\sf{No,}$

two numbers $\sf\color{red}{can \:not}$have $\sf\color{red}{18 \:as \:their\: HCF\: and \:380\: as\: LCM}$

$\small\textbf\color{orange}{Let the two numbers are a and b.}$

$\huge\sf{Given,}$

$\color{blue}\underline{\underline{ \tt{{ \boxed {LCM\: (a, b)\: = \:380} }}}}$

$\huge\sf{This\: implies, }$

$\color{blue}\underline{\underline{ \tt{{ \boxed {380\: is\: divisible \:by\: both\: a \:and \:b..(i).} }}}}$

$\huge\sf{Given, }$

$\color{violet}{\bf {HCF\: (a,\: b)\: =\: 18}}$

This implies, both a and b are divisible by 18..(ii).

$\underline{\boxed{\sf\purple{Combining\: (i) \:and \:(ii)}}}$

$\huge\sf{We\: get}$

$\underline{\boxed{\sf\purple{380\: is \:divisible \:by\: 18…(iii).}}}$

But, in actuality, 380 is not divisible by 18.

$\huge\sf{So,}$

$\Rrightarrow$the statement that two numbers have 18 as their HCF and 380 as their LCM is wrong

Thankyou :)

Answer 2

$\huge \ \: \red{answer}$

$\red{Since \: HCF \: is  \: 18  \: numbers \: can be \: assumed \: as  \: 18x  \: and  \: 18y}</p><p>[tex]⇒380 \: = \: 2 \: × \: 5 \: × \: 2 \: × \: 19$

$= 380 \:  is \: not \: divisible \: by  \: 18  \: itself \: hence \: HCF \:  18 \:  and \: LCM \: as  \: 380  \: is \: not \: possible.$

$\blue{i \: hope \: it \:helpfull \: for \: you}$