Question

Find the least number which when divided by $16,18,24$ leaves remainder $4$ but there is no remainder when it divide by $7$.

Answer 1

$LCM$ of $16,18,24$ is $720$

Hence the no. should be in the form of $720k+4$

As the no.s divisible by $7$

So, $720k+4=7k_1$

$⟹k_1=102K+\frac{6k+4}{7}$

Possible values such that $6k+4$ is divisible by $7$

$k=4$ Hence the required no. will be $720\times 4+4=2884$