Question

Find the least natural number which when divided by 25,40 and 60 leaves a remainder 8

Answer 1

$\Huge{ \boxed{Answer: }}$



$we \: \: have \: \: to \: \: first \: \: find \: \: the \\ LCM \: \: of \: 25, \: 40 \: \: and \: \: 60.$



LCM of 25, 40 & 60 = 2*2*2*5*5*3 = 8*25*3 = 200*3 = 600.

$\huge{ \boxed{LCM = 600.}}$


600 perfectly divides the 3 numbers and leaves the remainder as 0.


So, 600+8 = 608 is the smallest number which leaves remainder 8 when divided by 20, 40 & 60.



$\huge{ \boxed{ \therefore \: the \: \: number \: is \: \: 608.}}$

Answer 2

$let \: us \: first \: find \: out \: the \: least \\ \: number \: divisible \: by \: 25 \: and \\ \: 40 \: and \: 60. \\ \\ lcm \: = \: 600 \\ \\ so \: 600 \: is \: the \: smallest \: number \: which \: is \: exactly \\divisible \: by \: these \: numbers. \\ \\ but \: there \: should \: be \: 8 \: remaining \: as \: remainder. \: \\ \\ so\: the \: number \: is \: 600 + 8 = 608.$