Question

Find the smallest number which when divided by 8,9,10,15,20 gives a remainder of 5 every time. ​

Answer 1

$\bf{\underline{\underline{❥︎AnSweR:-}}}$

ʜᴇʀᴇ, ᴛʜᴇ sᴍᴀʟʟᴇsᴛ ɴᴜᴍʙᴇʀ ғᴏʀ ᴅɪᴠɪsɪᴏɴ ɪs ʟᴄᴍ ᴏғ 8, 9, 10,15 ᴀɴᴅ 20.

$\bf\fbox{8 = 2 x 2 x 2}$

$\bf\fbox{9 = 3 x 3}$

$\bf\fbox{10 = 2 x 5}$

$\bf\fbox{15 = 3 x 5}$

$\bf\fbox{20 = 2 x 2 x 5}$

ʟᴄᴍ ᴏғ ɢɪᴠᴇɴ ɴᴜᴍʙᴇʀs = 2 x 2 x 2 x 3 x 3 x 5 = 360

∴ ʀᴇǫᴜɪʀᴇᴅ, sᴍᴀʟʟᴇsᴛ ɴᴜᴍʙᴇʀ = ʟᴄᴍ + ʀᴇᴍᴀɪɴᴅᴇʀ = 360 + 5 = 365

$\bf\green{ ∴ The \: required</p><p> \: smallest \: number \: is \: 365.}$