What is the least common multiple of 9 and 12

Asked by admin @ in Mathematics viewed by 255 People

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.

Answered by admin @


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

12=2\times 2\times 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\times 2\times 2\times 3=24

Therefore the statement in option 1 is incorrect.

The factor of 6 and 9 are,

6=2\times 3

9=3\times 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\times 3\times 3=18

Therefore the statement in option 2 is correct.

The factor of 11 and 4 are,

11=1\times 11

4=2\times 2

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

Therefore the statement in option 3 is incorrect.

The factor of 9 and 10 are,

9=1\times 9

10=2\times 5

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

Therefore the statement in option 4 is correct.


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