# ISEE Upper Level Math : Numbers and Operations

## Example Questions

### Example Question #11 : How To Find The Least Common Multiple

What is the least common multiple of  and ?

Explanation:

Find all of the multiples of both numbers:

Find the first number that both sets have in common.

### Example Question #12 : How To Find The Least Common Multiple

Find the LCM of and

Explanation:

LCM is the least common multiple of the pair. There are a couple of terms at play here, so first find the LCM of 12 and 48. Since 12 goes into 48, 48 is the LCM. Then, look at xy and x. XY is the LCM between those two. So, multiply those together to get as your answer.

### Example Question #13 : How To Find The Least Common Multiple

What is the least common multiple of  and ?

Explanation:

A multiple of x is a number that results when x is multiplied by another whole number.

The least common multiple of two numbers is the smallest number that is a multiple of both the numbers.

24 is a multiple of 8 because 8 times 3 is 24.

24 is also a multiple of 12 because 12 times 2 is 24.

There are no numbers that are smaller than 24 which are also multiples of 8 and 12. Therefore, 24 is the least common multiple.

### Example Question #1 : Exponents

Simplify:

Explanation:

In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:

### Example Question #2 : Exponents

Evaluate:

Explanation:

In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:

Now they must be multiplied out before they can be added:

### Example Question #3 : Exponents

Subtract and simplify:

Explanation:

Consider a vertical subtraction process:

Rewrite as the addition of the opposite of the second expression, as follows:

### Example Question #4 : Exponents

Define an operation  as follows:

For all real numbers ,

Evaluate: .

Explanation:

, so

### Example Question #5 : Exponents

Subtract and simplify:

The correct answer is not among the other responses.

Explanation:

Consider a vertical subtraction process:

Rewrite as the addition of the opposite of the second expression, as follows:

### Example Question #1 : How To Subtract Exponents

Define an operation  as follows:

For all real numbers ,

Evaluate: .

Explanation:

### Example Question #7 : Exponents

Define an operation  as follows:

For all real numbers ,

Evaluate: