Question

Find the least number which when divided by $6,15$ and $18$ leave the remainder $5$ in each case.

Answer 1

Least number which when divided by $6,15$ and $18$ leave the remainder $0$

$=$LCM of $6,15,18$

So, LCM leaves remainder $0$

So, the Required number will be $5$ more than LCM

$\therefore$ Required number$=LCM+5$

Factors of $6=2\times 3$

Factors of $15=5\times 3$

Factors of $18=2\times 3\times 3$

$\therefore$ LCM$=2\times 3\times 3\times 5=90$

So, Required number$=LCM+5=90+5=95$