What is the lcm for 15 and 18

1. What is the LCM of 15, 20, 18?

Answer: LCM of 15, 20, 18 is 180.

2. What are the Factors of 180?

Answer: Factors of 180 are . There are integers that are factors of 180

3. How to Find the LCM of 15, 20, 18 ?

Least Common Multiple of 15, 20, 18.

Step 1: Divide all the numbers with common prime numbers having remainder zero.

Step 2: Then multiply all the prime factors with last row quotient of common division that is LCM(15, 20, 18) = 2 x 2 x 3 x 3 x 5 = 180.

What is the LCM and GCF of 15 and 18?


What is the lcm for 15 and 18
The question "What is the LCM and GCF of 15 and 18?" can be split into two questions: "What is the LCM of 15 and 18?" and "What is the GCF of 15 and 18?" In the question "What is the LCM and GCF of 15 and 18?", LCM is the abbreviation of Least Common Multiple and GCF is the abbreviation of Greatest Common Factor. To find the LCM, we first list the multiples of 15 and 18 and then we find the smallest multiple they have in common. To find the multiples of any number, you simply multiply the number by 1, then by 2, then by 3 and so on. Here is the beginning list of multiples of 15 and 18:

Multiples of 15: 15, 30, 45, 60, 75, 90, etc.

Multiples of 18: 18, 36, 54, 72, 90, 108, etc.

The least multiple on the two lists that they have in common is the LCM of 15 and 18. Therefore, the LCM of 15 and 18 is 90. To find the GCF, we first list the factors of 15 and 18 and then we find the largest factor they have in common. The factors of any number, are all the numbers that you can evenly divide into that number. In other words, the factors of 15 are all the numbers that can evenly divide into 15, and the factors of 18 are all the numbers that can evenly divide into 18. Here are the factors for 15 and 18:

Factors of 15: 1, 3, 5, and 15.

Factors of 18: 1, 2, 3, 6, 9, and 18.

The greatest factor on the two lists that they have in common is the GCF of 15 and 18. Therefore, the GCF of 15 and 18 is 3.

In summary, the answer to the question "What is the LCM and GCF of 15 and 18?" is 90 and 3.


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The lcm of 15 and 18 is the smallest positive integer that divides the numbers 15 and 18 without a remainder. Spelled out, it is the least common multiple of 15 and 18. Here you can find the lcm of 15 and 18, along with a total of three methods for computing it.

This Least Common Multiple Calculator is Really Cool! Click To TweetIn addition, we have a calculator you should check out. Not only can it determine the lcm of 15 and 18, but also that of three or more integers including fifteen and eighteen for example. Keep reading to learn everything about the lcm (15,18) and the terms related to it.

What is the LCM of 15 and 18

If you just want to know what is the least common multiple of 15 and 18, it is 90. Usually, this is written as

lcm(15,18) = 90

The lcm of 15 and 18 can be obtained like this:

  • The multiples of 15 are … , 75, 90, 105, ….
  • The multiples of 18 are …, 72, 90, 108, …
  • The common multiples of 15 and 18 are n x 90, intersecting the two sets above, .
  • In the intersection multiples of 15 ∩ multiples of 18 the least positive element is 90.
  • Therefore, the least common multiple of 15 and 18 is 90.

Taking the above into account you also know how to find all the common multiples of 15 and 18, not just the smallest. In the next section we show you how to calculate the lcm of fifteen and eighteen by means of two more methods.

How to find the LCM of 15 and 18

The least common multiple of 15 and 18 can be computed by using the greatest common factor aka gcf of 15 and 18. This is the easiest approach:

lcm (15,18) = = 90

Alternatively, the lcm of 15 and 18 can be found using the prime factorization of 15 and 18:

  • The prime factorization of 15 is: 3 x 5
  • The prime factorization of 18 is: 2 x 3 x 3
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(15,15) = 90

In any case, the easiest way to compute the lcm of two numbers like 15 and 18 is by using our calculator below. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 15,18. Push the button only to start over.

Similar searched terms on our site also include:

  • LCM of 15 and 23
  • LCM of 15 and 24
  • LCM of 15 and 25

Use of LCM of 15 and 18

What is the least common multiple of 15 and 18 used for? Answer: It is helpful for adding and subtracting fractions like 1/15 and 1/18. Just multiply the dividends and divisors by 6 and 5, respectively, such that the divisors have the value of 90, the lcm of 15 and 18.

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Properties of LCM of 15 and 18

The most important properties of the lcm(15,18) are:

  • Commutative property: lcm(15,18) = lcm(18,15)
  • Associative property: lcm(15,18,n) = lcm(lcm(18,15),n)

The associativity is particularly useful to get the lcm of three or more numbers; our calculator makes use of it.

To sum up, the lcm of 15 and 18 is 90. In common notation: lcm (15,18) = 90.

If you have been searching for lcm 15 and 18 or lcm 15 18 then you have come to the correct page, too. The same is the true if you typed lcm for 15 and 18 in your favorite search engine.

Note that you can find the least common multiple of many integer pairs including fifteen / eighteen by using the search form in the sidebar of this page.

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The LCM of 15 and 18 is 90.

Steps to find LCM

  1. Find the prime factorization of 15
    15 = 3 × 5
  2. Find the prime factorization of 18
    18 = 2 × 3 × 3
  3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

    LCM = 2 × 3 × 3 × 5

  4. LCM = 90

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What is the lcm for 15 and 18
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Find least common multiple (LCM) of: 30 & 36 45 & 54 5 & 6 75 & 90 105 & 126 30 & 18 15 & 36 45 & 18 15 & 54 75 & 18 15 & 90 105 & 18 15 & 126

Enter two numbers separate by comma. To find least common multiple (LCM) of more than two numbers, click here.

LCM of 15 and 18 is the smallest number among all common multiples of 15 and 18. The first few multiples of 15 and 18 are (15, 30, 45, 60, 75, 90, . . . ) and (18, 36, 54, 72, 90, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 18 - by division method, by prime factorization, and by listing multiples.

What is the LCM of 15 and 18?

Answer: LCM of 15 and 18 is 90.

What is the lcm for 15 and 18

Explanation:

The LCM of two non-zero integers, x(15) and y(18), is the smallest positive integer m(90) that is divisible by both x(15) and y(18) without any remainder.

Methods to Find LCM of 15 and 18

The methods to find the LCM of 15 and 18 are explained below.

  • By Listing Multiples
  • By Prime Factorization Method
  • By Division Method

LCM of 15 and 18 by Listing Multiples

What is the lcm for 15 and 18

To calculate the LCM of 15 and 18 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 15 (15, 30, 45, 60, 75, 90, . . . ) and 18 (18, 36, 54, 72, 90, . . . . )
  • Step 2: The common multiples from the multiples of 15 and 18 are 90, 180, . . .
  • Step 3: The smallest common multiple of 15 and 18 is 90.

∴ The least common multiple of 15 and 18 = 90.

LCM of 15 and 18 by Prime Factorization

Prime factorization of 15 and 18 is (3 × 5) = 31 × 51 and (2 × 3 × 3) = 21 × 32 respectively. LCM of 15 and 18 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 32 × 51 = 90.
Hence, the LCM of 15 and 18 by prime factorization is 90.

LCM of 15 and 18 by Division Method

What is the lcm for 15 and 18

To calculate the LCM of 15 and 18 by the division method, we will divide the numbers(15, 18) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 18.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 15 and 18. Write this prime number(2) on the left of the given numbers(15 and 18), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (15, 18) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
  • Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 15 and 18 is the product of all prime numbers on the left, i.e. LCM(15, 18) by division method = 2 × 3 × 3 × 5 = 90.

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LCM of 15 and 18 Examples

  1. Example 1: The product of two numbers is 270. If their GCD is 3, what is their LCM?

    Solution:

    Given: GCD = 3 product of numbers = 270 ∵ LCM × GCD = product of numbers ⇒ LCM = Product/GCD = 270/3 Therefore, the LCM is 90.

    The probable combination for the given case is LCM(15, 18) = 90.

  • Example 2: Verify the relationship between GCF and LCM of 15 and 18.

    Solution:

    The relation between GCF and LCM of 15 and 18 is given as, LCM(15, 18) × GCF(15, 18) = Product of 15, 18

    Prime factorization of 15 and 18 is given as, 15 = (3 × 5) = 31 × 51 and 18 = (2 × 3 × 3) = 21 × 32

    LCM(15, 18) = 90 GCF(15, 18) = 3 LHS = LCM(15, 18) × GCF(15, 18) = 90 × 3 = 270 RHS = Product of 15, 18 = 15 × 18 = 270 ⇒ LHS = RHS = 270

    Hence, verified.

  • Example 3: Find the smallest number that is divisible by 15 and 18 exactly.

    Solution:

    The smallest number that is divisible by 15 and 18 exactly is their LCM.
    ⇒ Multiples of 15 and 18:

    • Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, . . . .
    • Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, . . . .

    Therefore, the LCM of 15 and 18 is 90.

  • go to slidego to slidego to slide

    The LCM of 15 and 18 is 90. To find the LCM of 15 and 18, we need to find the multiples of 15 and 18 (multiples of 15 = 15, 30, 45, 60 . . . . 90; multiples of 18 = 18, 36, 54, 72 . . . . 90) and choose the smallest multiple that is exactly divisible by 15 and 18, i.e., 90.

    What is the Least Perfect Square Divisible by 15 and 18?

    The least number divisible by 15 and 18 = LCM(15, 18)
    LCM of 15 and 18 = 2 × 3 × 3 × 5 [Incomplete pair(s): 2, 5]
    ⇒ Least perfect square divisible by each 15 and 18 = LCM(15, 18) × 2 × 5 = 900 [Square root of 900 = √900 = ±30]
    Therefore, 900 is the required number.

    Which of the following is the LCM of 15 and 18? 90, 50, 12, 35

    The value of LCM of 15, 18 is the smallest common multiple of 15 and 18. The number satisfying the given condition is 90.

    If the LCM of 18 and 15 is 90, Find its GCF.

    LCM(18, 15) × GCF(18, 15) = 18 × 15 Since the LCM of 18 and 15 = 90 ⇒ 90 × GCF(18, 15) = 270

    Therefore, the GCF = 270/90 = 3.

    What are the Methods to Find LCM of 15 and 18?

    The commonly used methods to find the LCM of 15 and 18 are:

    • Division Method
    • Listing Multiples
    • Prime Factorization Method