Question

find the least number which when divided by 9,12 and 15, leaves 5 as the remainder in each case.

Answer 1

$\large\underline{\sf{Solution-}}$

Since, we have to find a least number which when divided by 9, 12 and 15, leaves 5 as the remainder in each case.

So, Let assume that 'x' be the least number which when divided by 9, 12 and 15, leaves 5 as the remainder in each case.

$\rm\implies \:x - 5 \: is \: divisible \: by \: 9$

$\rm\implies \:x - 5 \: is \: divisible \: by \: 12$

$\rm\implies \:x - 5 \: is \: divisible \: by \: 15$

So, it mean

$\rm\implies \:x - 5 \: is \: divisible \: by \: 9, \: 12, \: 15$

$\rm\implies \:x - 5 = LCM(9, 12, 15)$

Now, LCM ( 9, 12, 15 ) is

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{3}}}&{\underline{\sf{\:\:9\:, \: 12, \: \: 15\:\:}}}\\ {\underline{\sf{}}}& \underline{\sf{\:\:3\:, \: 4, \: \: 5 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

$\rm\implies \:LCM(9, 12, 15) = 3 \times 3 \times 4 \times 5 = 180$

So,

$\rm\implies \:x - 5 = 180$

$\rm\implies \:x = 180 + 5$

$\rm\implies \:x = 185$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

More to Know

1. LCM (a, b) × HCF (a, b) = a × b

2. LCM( a, b ) is always divisible by HCF( a, b ), a and b.

3. HCF (a, b) always divides a, b and LCM ( a, b )

Answer 2

Answer:

$\large\underline{\sf{Solution-}}$

Since, we have to find a least number which when divided by 9, 12 and 15, leaves 5 as the remainder in each case.

So, Let assume that 'x' be the least number which when divided by 9, 12 and 15, leaves 5 as the remainder in each case.

$\rm\implies \:x - 5 \: is \: divisible \: by \: 9$

$\rm\implies \:x - 5 \: is \: divisible \: by \: 12$

$\rm\implies \:x - 5 \: is \: divisible \: by \: 15$

So, it mean

$\rm\implies \:x - 5 \: is \: divisible \: by \: 9, \: 12, \: 15$

$\rm\implies \:x - 5 = LCM(9, 12, 15)$

Now, LCM ( 9, 12, 15 ) is

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{3}}}&{\underline{\sf{\:\:9\:, \: 12, \: \: 15\:\:}}}\\ {\underline{\sf{}}}& \underline{\sf{\:\:3\:, \: 4, \: \: 5 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

$\rm\implies \:LCM(9, 12, 15) = 3 \times 3 \times 4 \times 5 = 180$

So,

$\rm\implies \:x - 5 = 180$

$\rm\implies \:x = 180 + 5$

$\rm\implies \:x = 185$

$\purple{\rule{45pt}{7pt}}\red{\rule{45pt}{7pt}}\pink{\rule{45pt}{7pt}}\blue{\rule{45pt}{7pt}}$