discover the Least typical Multiple (LCM) of 2 NumbersPractice renders Perfect

## Find the Least typical Multiple (LCM) of 2 Numbers

One the the factors we look at multiples and also primes is to use these methods to discover the least common multiple of two numbers. This will certainly be helpful when we include and subtract fountain with different denominators.

You are watching: What is the least common denominator of 15 and 20

### Listing Multiples Method

A usual multiple of two numbers is a number that is a many of both numbers. Expect we want to find typical multiples of 10 and also 25. We can list the first several multiples of each number. Then us look for multiples the are common to both lists—these room the usual multiples.

<eginsplit 10 & colon ; 10, 20, 30, 40, extbf50, 60, 70, 80, 90, extbf100, 110, ldots \ 25 & colon ; 25, extbf50, 75, extbf100, 125, ldots endsplit onumber >

We check out that (50) and (100) show up in both lists. They are usual multiples of (10) and (25). We would find more common multiples if we continued the list of multiples because that each.

The the smallest number the is a multiple of 2 numbers is called the least usual multiple (LCM). So the the very least LCM that (10) and (25) is (50).

### Prime factors Method

Another method to discover the least typical multiple of 2 numbers is to usage their element factors. We’ll usage this an approach to find the LCM of (12) and also (18).

We start by detect the prime factorization of each number.

<12 = 2 cdot 2 cdot 3 qquad qquad 18 = 2 cdot 3 cdot 3 onumber>

Then we compose each number together a product that primes, equivalent primes vertically when possible.

<eginsplit 12 & = 2 cdot 2 cdot 3 \ 18 & = 2 cdot quad ; 3 cdot 3 endsplit onumber >

Now we bring down the primes in each column. The LCM is the product of these factors.

Example (PageIndex7): lcm

Find the LCM that (50) and (100) utilizing the prime components method.

Solution

 Write the prime factorization of every number. (50 = 2 cdot 5 cdot 5 qquad 100 = 2 cdot 2 cdot 5 cdot 5) Write each number together a product that primes, matching primes vertically when possible. (eginsplit 50 & = quad ; 2 cdot 5 cdot 5 \ 100 & = 2 cdot 2 cdot 5 cdot 5 endsplit) Bring down the primes in every column. Multiply the factors to gain the LCM.See more: How Many Tips Does A Quad Cane Base Have ? Tips & Advice Center: Canes Tips LCM = 2 • 2 • 5 • 5 The LCM that 50 and 100 is 100.

Exercise (PageIndex14)

Find the LCM using the prime determinants method: (60, 72)

prize

(360)
The text passage describes methods for finding the least common multiple (LCM) of 2 numbers, including the listing multiples method and the prime factors method. It provides an example of finding the LCM of 50 and 100 using the prime factors method and provides the answer.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
discover the Least typical Multiple (LCM) of 2 NumbersPractice renders Perfect

## Find the Least typical Multiple (LCM) of 2 Numbers

One the the factors we look at multiples and also primes is to use these methods to discover the least common multiple of two numbers. This will certainly be helpful when we include and subtract fountain with different denominators.

You are watching: What is the least common denominator of 15 and 20

### Listing Multiples Method

A usual multiple of two numbers is a number that is a many of both numbers. Expect we want to find typical multiples of 10 and also 25. We can list the first several multiples of each number. Then us look for multiples the are common to both lists—these room the usual multiples.

<eginsplit 10 & colon ; 10, 20, 30, 40, extbf50, 60, 70, 80, 90, extbf100, 110, ldots \ 25 & colon ; 25, extbf50, 75, extbf100, 125, ldots endsplit onumber >

We check out that (50) and (100) show up in both lists. They are usual multiples of (10) and (25). We would find more common multiples if we continued the list of multiples because that each.

The the smallest number the is a multiple of 2 numbers is called the least usual multiple (LCM). So the the very least LCM that (10) and (25) is (50).

### Prime factors Method

Another method to discover the least typical multiple of 2 numbers is to usage their element factors. We’ll usage this an approach to find the LCM of (12) and also (18).

We start by detect the prime factorization of each number.

<12 = 2 cdot 2 cdot 3 qquad qquad 18 = 2 cdot 3 cdot 3 onumber>

Then we compose each number together a product that primes, equivalent primes vertically when possible.

<eginsplit 12 & = 2 cdot 2 cdot 3 \ 18 & = 2 cdot quad ; 3 cdot 3 endsplit onumber >

Now we bring down the primes in each column. The LCM is the product of these factors.

Example (PageIndex7): lcm

Find the LCM that (50) and (100) utilizing the prime components method.

Solution

 Write the prime factorization of every number. (50 = 2 cdot 5 cdot 5 qquad 100 = 2 cdot 2 cdot 5 cdot 5) Write each number together a product that primes, matching primes vertically when possible. (eginsplit 50 & = quad ; 2 cdot 5 cdot 5 \ 100 & = 2 cdot 2 cdot 5 cdot 5 endsplit) Bring down the primes in every column. Multiply the factors to gain the LCM.See more: How Many Tips Does A Quad Cane Base Have ? Tips & Advice Center: Canes Tips LCM = 2 • 2 • 5 • 5 The LCM that 50 and 100 is 100.

Exercise (PageIndex14)

Find the LCM using the prime determinants method: (60, 72)

prize

(360)
user
The text passage describes methods for finding the least common multiple (LCM) of 2 numbers, including the listing multiples method and the prime factors method. It provides an example of finding the LCM of 50 and 100 using the prime factors method and provides the answer.

TYPE: SINGLE_QUESTION_WITH_ANSWER