Question

What is the least number which when divided by $7,9$ and $12$, leaves the same remainder $1$ in each case?

• A. $253$
• B. $352$
• C. $505$
• D. $523$

Answer 1

Answer: (A)

$253$

$7=7\times 1$
$9=3\times 3$
$12=2\times 2\times 3$
$\therefore$ L.C.M of $7,9,12$= $2\times 2\times 3\times 3\times 3=252$

Add 1 to the LCM to get a remainder of 1 when the number is divided by any of the 3 given numbers - 7, 9, 12.
So the number will be $252+1=253$