Answer: The statements in options 2 and 4 are true.
Explanation:
The LCM of two numbers is the smallest number that is multiple of both numbers.
The factor of 8 and 12 are,
![8=2\times 2\times 2](https://tex.z-dn.net/?f=8%3D2%5Ctimes%202%5Ctimes%202)
![12=2\times 2\times 3](https://tex.z-dn.net/?f=12%3D2%5Ctimes%202%5Ctimes%203)
Since 2 and 2 are common in both but 2 and 3 are not same, therefore the L.C.M. of 8 and 12 is,
![L.C.M.(8,12)=2\times 2\times 2\times 3=24](https://tex.z-dn.net/?f=L.C.M.%288%2C12%29%3D2%5Ctimes%202%5Ctimes%202%5Ctimes%203%3D24)
Therefore the statement in option 1 is incorrect.
The factor of 6 and 9 are,
![6=2\times 3](https://tex.z-dn.net/?f=6%3D2%5Ctimes%203)
![9=3\times 3](https://tex.z-dn.net/?f=9%3D3%5Ctimes%203)
Since 3 is common in both but 2 and 3 are not same, therefore the L.C.M. of 6 and 9 is,
![L.C.M.(6,9)=2\times 3\times 3=18](https://tex.z-dn.net/?f=L.C.M.%286%2C9%29%3D2%5Ctimes%203%5Ctimes%203%3D18)
Therefore the statement in option 2 is correct.
The factor of 11 and 4 are,
![11=1\times 11](https://tex.z-dn.net/?f=11%3D1%5Ctimes%2011)
![4=2\times 2](https://tex.z-dn.net/?f=4%3D2%5Ctimes%202)
Since all factor are different, therefore the L.C.M. of 11 and 4 is,
![L.C.M.(11,4)=1\times 11\times 2\times 2=44](https://tex.z-dn.net/?f=L.C.M.%2811%2C4%29%3D1%5Ctimes%2011%5Ctimes%202%5Ctimes%202%3D44)
Therefore the statement in option 3 is incorrect.
The factor of 9 and 10 are,
![9=1\times 9](https://tex.z-dn.net/?f=9%3D1%5Ctimes%209)
![10=2\times 5](https://tex.z-dn.net/?f=10%3D2%5Ctimes%205)
Since all factor are different, therefore the L.C.M. of 9 and 10 is,
![L.C.M.(9,10)=1\times 9\times 2\times 5=90](https://tex.z-dn.net/?f=L.C.M.%289%2C10%29%3D1%5Ctimes%209%5Ctimes%202%5Ctimes%205%3D90)
Therefore the statement in option 4 is correct.