How to find the least common multiple

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ISEE Upper Level Quantitative Reasoning › How to find the least common multiple

Questions 1 - 10
1

Which of the following is the least common multiple of 6, 9, and 12?

36

12

18

648

Explanation

The least common multiple is the smallest number in value that is a multiple of all three of the numbers. The best way to find the least common multiple (LCM) is to make a quick list of the first few multiples of each number, and then identify the smallest number that is common to all three lists.

Multiples are numbers that you get when multiplying the original number by other numbers.

18 is an answer choice that is common to both 6 and 9, but it is not also a multiple of 12, so it is not correct.

The smallest value that is a common multiple of all three is 36, so this is the LCM.

While 648 is a multiple of all three numbers, it is not the least common multiple of the three numbers.

2

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.

3

What is the least common multiple of 4, 12, and 16?

Explanation

To find the least common multiple, you need to determine the multiple that all three numbers share that is of the least value. List the multiples of each number and identify the first number (least value) that is in both lists:

The LCM of 4, 12, and 16 is 48 since it is the first number that shows up in all three lists.

4

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.

5

What is the least common multiple of 16 and 20?

Explanation

is the lowest number that is a multiple of both 16 and 20, so we see which is the first number that appears in both lists of multiples.

The multiples of 16:

The multiples of 20:

6

What is the least common multiple of and ?

Explanation

Find all of the factors of both 9 and 6:

Eliminate all factors that 9 and 6 have in common, in this instance 3 (only eliminate the repeated instance). Multiply all factors that are not in common:

7

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.

8

What is the least common multiple of 15 and 18?

Explanation

To find the least common multiple, you need to determine the multiple that both numbers share that is of the least value. List the multiples of each number and identify the first number (least value) that is in both lists:

The LCM of 15 and 18 is 90 since it is the first number that shows up in both lists.

9

Which of the following values of makes this statement true?

All answer choices are correct.

Explanation

For to be a true statement, must be a multiple of . Each of the four values given is divisible by , as seen below:

10

Which of the following values of makes this statement false?

Explanation

For to be true, must be a factor of . Of the five choices, all are factors of except for . This is the correct choice.

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