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Here are some clues to a mystery number.

One of my factors is 4 .
When you pair me with 32 , we have an LCM of 32 .
I am greater than 4 and less than 15 .

What is the mystery number?
The mystery number is
◻

Here are some clues to a mystery number. $\newline$ - One of my factors is $4$ . $\newline$ - When you pair me with $32$ , we have an LCM of $32$ . $\newline$ - I am greater than $4$ and less than $15$ . $\newline$ What is the mystery number? $\newline$ The mystery number is $\square$

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Write and solve direct variation equations

Full solution

Q. Here are some clues to a mystery number.

\newline

- One of my factors is

4

.

\newline

- When you pair me with

32

, we have an LCM of

32

.

\newline

- I am greater than

4

and less than

15

.

\newline

What is the mystery number?

\newline

The mystery number is

\square

Factor Clue: One of the clues is that the mystery number has a factor of $4$ . So, the mystery number could be $4$ , $8$ , or $12$ since these are greater than $4$ and less than $15$ .
LCM Clue: Another clue is that when paired with $32$ , the LCM is $32$ . This means the mystery number must be a factor of $32$ .
Elimination of $4$ : Checking the possible numbers, $4$ and $8$ are factors of $32$ . But since the LCM with $32$ must be $32$ itself, the mystery number can't be $4$ because the LCM of $4$ and $32$ is $32$ , which means the mystery number is $8$ .
Final Mystery Number: The mystery number is $8$ , which is greater than $4$ and less than $15$ , has $4$ as a factor, and has an LCM of $32$ when paired with $32$ .

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