On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 12 and 18. Show
Follow the steps below, and let's calculate the LCM of 12 and 18. Method 1 - Prime factorizationStep 1: Create a list of all the prime factors of the numbers 12 and 18:
The prime factors of 12 are 2, 2 and 3. Prime factorization of 12 in exponential form is: 12 = 22x31
The prime factors of 18 are 2, 3 and 3. Prime factorization of 18 in exponential form is: 18 = 21x32 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 12 and 18. The Least Common Multiple of 12 and 18 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 12:Multiples of 18:Therefore,
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 12 and 18 is 36. LCM(12,18) = 36 Least Common Multiple of 12 and 18 with GCF FormulaThe formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b). GCF(12,18) = 6 LCM(12,18) = ( 12 × 18) / 6 LCM(12,18) = 216 / 6 LCM(12,18) = 36 Least Common Multiple (LCM) of 12 and 18 with PrimesLeast common multiple can be found by multiplying the highest exponent prime factors of 12 and 18. First we will calculate the prime factors of 12 and 18. Prime Factorization of 12
Prime factors of 12 are 2, 3. Prime factorization of 12 in exponential form is: 12 = 22 × 31 Prime Factorization of 18
Prime factors of 18 are 2, 3. Prime factorization of 18 in exponential form is: 18 = 21 × 32 Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 18. LCM(12,18) = 22 × 32 The LCM of 12 and 18 is 36. Steps to find LCM
MathStep (Works offline) Download our mobile app and learn how to find LCM of upto four numbers in your own time:Android and iPhone/ iPad Find least common multiple (LCM) of: 24 & 36 6 & 9 36 & 54 4 & 6 60 & 90 84 & 126 24 & 18 12 & 36 36 & 18 12 & 54 60 & 18 12 & 90 84 & 18 12 & 126 Enter two numbers separate by comma. To find least common multiple (LCM) of more than two numbers, click here.
LCM of 12 and 18 is the smallest number among all common multiples of 12 and 18. The first few multiples of 12 and 18 are (12, 24, 36, 48, 60, 72, 84, . . . ) and (18, 36, 54, 72, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 18 - by listing multiples, by prime factorization, and by division method. What is the LCM of 12 and 18?Answer: LCM of 12 and 18 is 36. Explanation: The LCM of two non-zero integers, x(12) and y(18), is the smallest positive integer m(36) that is divisible by both x(12) and y(18) without any remainder. Methods to Find LCM of 12 and 18Let's look at the different methods for finding the LCM of 12 and 18.
LCM of 12 and 18 by Division MethodTo calculate the LCM of 12 and 18 by the division method, we will divide the numbers(12, 18) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 18.
The LCM of 12 and 18 is the product of all prime numbers on the left, i.e. LCM(12, 18) by division method = 2 × 2 × 3 × 3 = 36. LCM of 12 and 18 by Prime FactorizationPrime factorization of 12 and 18 is (2 × 2 × 3) = 22 × 31 and (2 × 3 × 3) = 21 × 32 respectively. LCM of 12 and 18 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 32 = 36. LCM of 12 and 18 by Listing MultiplesTo calculate the LCM of 12 and 18 by listing out the common multiples, we can follow the given below steps:
∴ The least common multiple of 12 and 18 = 36. ☛ Also Check:
LCM of 12 and 18 Examples
Example 2: The product of two numbers is 216. If their GCD is 6, what is their LCM? Solution: Given: GCD = 6 product of numbers = 216 ∵ LCM × GCD = product of numbers ⇒ LCM = Product/GCD = 216/6 Therefore, the LCM is 36. The probable combination for the given case is LCM(12, 18) = 36.
Example 3: Verify the relationship between GCF and LCM of 12 and 18. Solution: The relation between GCF and LCM of 12 and 18 is given as, LCM(12, 18) × GCF(12, 18) = Product of 12, 18 Prime factorization of 12 and 18 is given as, 12 = (2 × 2 × 3) = 22 × 31 and 18 = (2 × 3 × 3) = 21 × 32 LCM(12, 18) = 36 GCF(12, 18) = 6 LHS = LCM(12, 18) × GCF(12, 18) = 36 × 6 = 216 RHS = Product of 12, 18 = 12 × 18 = 216 ⇒ LHS = RHS = 216Hence, verified. go to slidego to slidego to slide
The LCM of 12 and 18 is 36. To find the LCM (least common multiple) of 12 and 18, we need to find the multiples of 12 and 18 (multiples of 12 = 12, 24, 36, 48; multiples of 18 = 18, 36, 54, 72) and choose the smallest multiple that is exactly divisible by 12 and 18, i.e., 36. What is the Least Perfect Square Divisible by 12 and 18?The least number divisible by 12 and 18 = LCM(12, 18) If the LCM of 18 and 12 is 36, Find its GCF.LCM(18, 12) × GCF(18, 12) = 18 × 12 Since the LCM of 18 and 12 = 36 ⇒ 36 × GCF(18, 12) = 216 Therefore, the greatest common factor (GCF) = 216/36 = 6. How to Find the LCM of 12 and 18 by Prime Factorization?To find the LCM of 12 and 18 using prime factorization, we will find the prime factors, (12 = 2 × 2 × 3) and (18 = 2 × 3 × 3). LCM of 12 and 18 is the product of prime factors raised to their respective highest exponent among the numbers 12 and 18. Which of the following is the LCM of 12 and 18? 36, 10, 12, 2The value of LCM of 12, 18 is the smallest common multiple of 12 and 18. The number satisfying the given condition is 36. |