What is the LCM and GCF of 9 and 12? Show
Multiples of 9: 9, 18, 27, 36, 45, 54, etc. Multiples of 12: 12, 24, 36, 48, 60, 72, etc. The least multiple on the two lists that they have in common is the LCM of 9 and 12. Therefore, the LCM of 9 and 12 is 36. To find the GCF, we first list the factors of 9 and 12 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 9 are all the numbers that can evenly divide into 9, and the factors of 12 are all the numbers that can evenly divide into 12. Here are the factors for 9 and 12:Factors of 9: 1, 3, and 9. Factors of 12: 1, 2, 3, 4, 6, and 12. The greatest factor on the two lists that they have in common is the GCF of 9 and 12. Therefore, the GCF of 9 and 12 is 3.In summary, the answer to the question "What is the LCM and GCF of 9 and 12?" is 36 and 3. LCM and GCF Calculator Do you need the LCM and GCF for another set of numbers? No problem, please enter them below: What is the LCM and GCF of 9 and 13? Here is the next LCM and GCF question on our list that we have tackled! Copyright | Privacy Policy | Disclaimer | Contact
On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 9 and 12. Follow the steps below, and let's calculate the LCM of 9 and 12. Method 1 - Prime factorizationStep 1: Create a list of all the prime factors of the numbers 9 and 12:
The prime factors of 9 are 3 and 3. Prime factorization of 9 in exponential form is: 9 = 32
The prime factors of 12 are 2, 2 and 3. Prime factorization of 12 in exponential form is: 12 = 22x31 Step 2: Identify the highest power of each prime number from the above boxes:Step 3: Multiply these values together:Step 4: The result:
As seen on the calculation above, we have now obtained the LCM of 9 and 12. The Least Common Multiple of 9 and 12 is 36. Method 2 - List of MultiplesFind and list multiples of each number until the first common multiple is found. This is the lowest common multiple. Multiples of 9:
9, 18, 27, 36, 45, 54, 63 Multiples of 12:Therefore,The full form of LCM is Least Common Multiple and also noted as Lowest Common Multiple (LCM) or Least Common Divisor (LCD). LCM is the smallest positive integer that is equally divisible by two integers a and b. It is denoted as LCM(a,b). For example, if you take integer a=8 and b=12, the LCM(a,b) i.e., LCM(8,12)=24. Use this free online LCM Calculator and provide the input numbers that are given to calculate the LCM of two integers. Give the first input in the number 1 field and then second input in the number 2 field and press on the ‘Calculate’ button which is colored in blue. Remember not to use commas within your numbers like 5,000, 7,500. Ex: LCM of 44 and 60 (or) LCM of 45 and 30 (or) LCM of 32 and 48 Here are some samples of LCM of two numbers calculations. The LCM of 9 and 12 is 36. Steps to find LCM
MathStep (Works offline) Android and iPhone/ iPad Find least common multiple (LCM) of: 18 & 24 27 & 36 3 & 4 45 & 60 63 & 84 18 & 12 9 & 24 27 & 12 9 & 36 45 & 12 9 & 60 63 & 12 9 & 84 Enter two numbers separate by comma. To find least common multiple (LCM) of more than two numbers, click here.
Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.
Least common multiple (LCM) of 9 and 12 is 36. LCM(9,12) = 36 Least Common Multiple of 9 and 12 with GCF FormulaThe formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b). GCF(9,12) = 3 LCM(9,12) = ( 9 × 12) / 3 LCM(9,12) = 108 / 3 LCM(9,12) = 36 Least Common Multiple (LCM) of 9 and 12 with PrimesLeast common multiple can be found by multiplying the highest exponent prime factors of 9 and 12. First we will calculate the prime factors of 9 and 12. Prime Factorization of 9
Prime factors of 9 are 3. Prime factorization of 9 in exponential form is: 9 = 32 Prime Factorization of 12
Prime factors of 12 are 2, 3. Prime factorization of 12 in exponential form is: 12 = 22 × 31 Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 12. LCM(9,12) = 32 × 22
LCM of 9 and 12 is the smallest number among all common multiples of 9 and 12. The first few multiples of 9 and 12 are (9, 18, 27, 36, 45, . . . ) and (12, 24, 36, 48, 60, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 12 - by division method, by listing multiples, and by prime factorization. What is the LCM of 9 and 12?Answer: LCM of 9 and 12 is 36. Explanation: The LCM of two non-zero integers, x(9) and y(12), is the smallest positive integer m(36) that is divisible by both x(9) and y(12) without any remainder. Methods to Find LCM of 9 and 12The methods to find the LCM of 9 and 12 are explained below.
LCM of 9 and 12 by Listing MultiplesTo calculate the LCM of 9 and 12 by listing out the common multiples, we can follow the given below steps:
∴ The least common multiple of 9 and 12 = 36. LCM of 9 and 12 by Division MethodTo calculate the LCM of 9 and 12 by the division method, we will divide the numbers(9, 12) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 12.
The LCM of 9 and 12 is the product of all prime numbers on the left, i.e. LCM(9, 12) by division method = 2 × 2 × 3 × 3 = 36. LCM of 9 and 12 by Prime FactorizationPrime factorization of 9 and 12 is (3 × 3) = 32 and (2 × 2 × 3) = 22 × 31 respectively. LCM of 9 and 12 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 32 = 36. ☛ Also Check:
Example 2: The product of two numbers is 108. If their GCD is 3, what is their LCM? Solution: Given: GCD = 3 product of numbers = 108 ∵ LCM × GCD = product of numbers ⇒ LCM = Product/GCD = 108/3 Therefore, the LCM is 36. The probable combination for the given case is LCM(9, 12) = 36.
Example 3: The GCD and LCM of two numbers are 3 and 36 respectively. If one number is 12, find the other number. Solution: Let the other number be y. Therefore, the other number is 9. go to slidego to slidego to slide
The LCM of 9 and 12 is 36. To find the least common multiple of 9 and 12, we need to find the multiples of 9 and 12 (multiples of 9 = 9, 18, 27, 36; multiples of 12 = 12, 24, 36, 48) and choose the smallest multiple that is exactly divisible by 9 and 12, i.e., 36. What is the Relation Between GCF and LCM of 9, 12?The following equation can be used to express the relation between GCF and LCM of 9 and 12, i.e. GCF × LCM = 9 × 12. Which of the following is the LCM of 9 and 12? 50, 15, 45, 36The value of LCM of 9, 12 is the smallest common multiple of 9 and 12. The number satisfying the given condition is 36. If the LCM of 12 and 9 is 36, Find its GCF.LCM(12, 9) × GCF(12, 9) = 12 × 9 Since the LCM of 12 and 9 = 36 ⇒ 36 × GCF(12, 9) = 108 Therefore, the GCF = 108/36 = 3. What are the Methods to Find LCM of 9 and 12?The commonly used methods to find the LCM of 9 and 12 are:
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