Question

The HCF and LCM of two numbers are 6 and 864 respectively. If one number is 96,
find the other number.
(1) 84
(2) 45
(3) 54
(4) 24
​

Answer 1

$\large \boxed{\boxed{ \blue{ᴀɴsᴡᴇʀ}}}$

ʜᴄғ = 6

ʟᴄᴍ = 864

ʟᴇᴛ ᴏɴᴇ ɴᴜᴍʙᴇʀ ʙᴇ ᴀ = 96

ʟᴇᴛ ᴀɴᴏᴛʜᴇʀ ɴᴜᴍʙᴇʀ ʙᴇ ʙ

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

ʜᴄғ × ʟᴄᴍ = ᴀ × ʙ

6 × 864 = 96 × ʙ

ʙ = 6 × 864 / 96

ʙ = 5184/96

ʙ = 54

(3) 54 ɪs ᴛʜᴇ ᴀɴsᴡᴇʀ

Answer 2

$\large{\mathfrak{ \orange{Solution : }}}$

$\tt{\blue{ʜᴄғ = 6}}$

$\tt{ \blue{ʟᴄᴍ = 864}}$

$\tt{ \blue{ʟᴇᴛ \: ᴏɴᴇ \: ɴᴜᴍʙᴇʀ \: ʙᴇ \: ᴀ = 96}}$

$\tt{ \blue{ʟᴇᴛ \: ᴀɴᴏᴛʜᴇʀ \: ɴᴜᴍʙᴇʀ \: ʙᴇ \: ʙ}}$

$\sf{ \green{We \: know \: that,}}$

$\tt{ \purple{ʜᴄғ × ʟᴄᴍ = ᴀ × ʙ}}$

$\tt{ \purple{ 6 × 864 = 96 × ʙ}}$

$\tt{ \purple{ʙ = 6 × 864 / 96}}$

$\tt{ \purple{ʙ = 5184/96}}$

$\tt{ \red{ \underline{ʙ = 54}}}$

Hence, the answer is 54 (option 3.) ${\boxed{\pink{\checkmark}}}$