Question

ᴛʜᴇ HCF ᴀɴᴅ LCM ᴏғ ᴛᴡᴏ ɴᴜᴍʙᴇʀs ᴀʀᴇ 12 ᴀɴᴅ 5040 , ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ . ɪғ ᴏɴᴇ ᴏғ ᴛʜᴇ ɴᴜᴍʙᴇʀs ɪs 144 , ғɪɴᴅ ᴛʜᴇ ᴏᴛʜᴇʀ ɴᴜᴍʙᴇʀ?​

Answer 1

$\begin{gathered} \bold{ \pmb{GiVEN}} \\ \red{ \tt HCF \: of \: two \: numbers} = 12 \\ \tt \red{ \: LCM \: of \: two \: number} = 5040 \\ \tt \red{ \: One \: number }= 144 \\ \\ \\ \bold{\pmb{TO \: \: FiND}} \\ \bf{ \: Other \: number} \\ \\ \\ \bold{ \pmb{SOLUTiON}} \\ \\ \small{\boxed{\cal{LCM \times HCF = Product \: of \: two \: numbers}}} \\ \\ \sf \: Let \: the \: other \: number \: be \: b \\ \rm 12 \times 5040 = 144 \times b \\ \rm 60480 = 144b \\ \rm \: b = \dfrac{60480}{144} \\ \\ \boxed{\bold {\pmb{\blue{\underline{ \dag \: \: Other \: \: number = 420}}}}}\end{gathered}$

Answer 2

Given HCF=12,LCM=5040

and also one number is 144

Let the other number be x

As we know that

Product of two numbers is HCF×LCM

⟹144×x=12×5040

⟹x=420

The other number is 420