Question

Solve the following:
(i) Find the lowest number which leaves $4$ as remainder when divide by $9$ and $12.$
(ii) Find the lowest number which being increased by $3$ is exactly divided by $9$ and $12$

Answer 1

(i) here, lcm of 9 and 12=36

the lowest number divisible 9 and 12 is 36.

$\therefore$ Adding 4 to 36 we get 40.

Hence the required number is 40, which gives remainder 4 when divided by 9 and 12.

(ii) here,

lcm of 9 and 12=36

subtracting the lcm by 3 we get 33.

Thus the required number is 33, which is exactly divisible by 9 and 12 when increased by 3.