Question

Which of the following statements are true? Select all that apply.

The least common multiple of 8 and 12 is 48.
The least common multiple of 6 and 9 is 18.
The least common multiple of 11 and 4 is 1.
The least common multiple of 9 and 10 is 90.

Answer 1

Options 2 and 4 are correct

Step-by-step explanation:

Answer 2

Answer: The statements in options 2 and 4 are true.

Step-by-step 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* 2* 2`

`12=2* 2* 3`

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* 2* 2* 3=24`

Therefore the statement in option 1 is incorrect.

The factor of 6 and 9 are,

`6=2* 3`

`9=3* 3`

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* 3* 3=18`

Therefore the statement in option 2 is correct.

The factor of 11 and 4 are,

`11=1* 11`

`4=2* 2`

Since all factor are different, therefore the L.C.M. of 11 and 4 is,

`L.C.M.(11,4)=1* 11* 2* 2=44`

Therefore the statement in option 3 is incorrect.

The factor of 9 and 10 are,

`9=1* 9`

`10=2* 5`

Since all factor are different, therefore the L.C.M. of 9 and 10 is,

`L.C.M.(9,10)=1* 9* 2* 5=90`

Therefore the statement in option 4 is correct.