Question

Find the least number which when divided by $12,16,24$ and $36$ leaves a remainder $7$ in each case.

Answer 1

Least number when divided by $12,16,24,36$ and leaves remainder $0$

$=$LCM of $12,16,24,36$

So,LCM leaves remainder $0$

So,Required number will be $7$ more than LCM

$\therefore$ Required number$=LCM+7$

Factors of $12=2\times 3\times 2$

Factors of $16=2\times 2\times 2\times 2$

Factors of $24=2\times 2\times 2\times 3$

Factors of $36=2\times 2\times 3\times 3$

$\therefore$ LCM$=2\times 2\times 2\times 2\times 3\times 3=16\times 9=144$

So,Required number$=LCM+7=144+7=151$