Question

The least number which when decreased by $7$ is exactly divisible by $2,16,18,21$ and $28$ is

• A. $1012$
• B. $1008$
• C. $1015$
• D. $1022$

Answer 1

The correct option is C $1015$

To find such a number we will evaluate $LCM$ of $2,16,18,21,28$ so, that it will be divisible by each one of them then we will add $7$ in the resulting number to obtain the desired result.

$2=2$

$16=2\times 2\times 2\times 2$

$18=2\times 3\times 3$

$21=3\times 7$

$28=2\times 2\times 7$

So, $LCM=2\times 2\times 2\times 2\times 3\times 3\times 7$

$=16\times 9\times 7$

$=1008$

Now, add $7$ to the $LCM$ of all numbers to get the desired result,

$1008+7=1015$

Hence, option $C$ is correct.