Question

Determine the greatest $3-$ digit number which is exactly divisible by $8,10$ and $12$

Answer 1

Smallest number divisible by $8,10,12=$L.C.M of $8,10,12$

Factors of $8=1\times 2\times 2\times 2$

Factors of $10=1\times 2\times 5$

Factors of $12=1\times 2\times 3\times 2$

So, L.C.M$=2\times 2\times 2\times 3\times 5=120$

$\therefore 120$ is the smallest number divisible by $8,10,12$

Now, we need to find greatest $3-$ digit number divisible by $8,10,12$

Greatest $3$ digit number$=999$

$999=120\times 8+39$

So, remainder is $39$

$\therefore$ Required number$=999-39=960$

So, $960$ is the greatest $3-$ digit number.