Question

Find a number which has a multiple of all the numbers from 1 to 10?

• A. $5040$
• B. $1260$
• C. $720$
• D. $1440$

Answer 1

The correct option is A $5040$

Number which has a multiple of all the numbers from $1$ to $10$ will be multiple of their LCM.

$LCM(1,2,3,4,5,6,7,8,9,10)=$

$1=1$

$2=1\times 2$

$3=1\times 3$

$4=1\times 2\times 2$

$5=1\times 5$

$6=1\times 2\times 3$

$7=1\times 7$

$8=1\times 2\times 2\times 2$

$9=1\times 3\times 3$

$10=1\times 2\times 5$

$\therefore LCM=1\times 2\times 2\times 2\times 3\times 3\times 5\times 7=2520$

Amongst the given options, only $5040$ is a multiple of $2520$.

Hence, $5040$ is a multiple of all the numbers from $1$ to $10$.