The least common multiple is the product of all factors in the greatest number of their occurrence. Show
LCM = LCM = LCM = 756 The least common multiple of 36, 54 and 63 is 756. 1. What is the LCM of 36 and 54? Answer: LCM of 36 and 54 is 108. 2. What are the Factors of 36? Answer: Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. There are 9 integers that are factors of 36. The greatest factor of 36 is 36. 3. What are the Factors of 54? Answer: Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. There are 8 integers that are factors of 54. The greatest factor of 54 is 54. 4. How to Find the LCM of 36 and 54? Answer: Least Common Multiple of 36 and 54 = 108 Step 1: Find the prime factorization of 36 36 = 2 x 2 x 3 x 3 Step 2: Find the prime factorization of 54 54 = 2 x 3 x 3 x 3 Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm: LCM = 108 = 2 x 2 x 3 x 3 x 3 Step 4: Therefore, the least common multiple of 36 and 54 is 108.
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 36 and 54 is 108. LCM(36,54) = 108 Least Common Multiple of 36 and 54 with GCF FormulaThe formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b). GCF(36,54) = 18 LCM(36,54) = ( 36 × 54) / 18 LCM(36,54) = 1944 / 18 LCM(36,54) = 108 Least Common Multiple (LCM) of 36 and 54 with PrimesLeast common multiple can be found by multiplying the highest exponent prime factors of 36 and 54. First we will calculate the prime factors of 36 and 54. Prime Factorization of 36
Prime factors of 36 are 2, 3. Prime factorization of 36 in exponential form is: 36 = 22 × 32 Prime Factorization of 54
Prime factors of 54 are 2, 3. Prime factorization of 54 in exponential form is: 54 = 21 × 33 Now multiplying the highest exponent prime factors to calculate the LCM of 36 and 54. LCM(36,54) = 22 × 33 The first step to this method of finding the Least Common Multiple of 36 and 54 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number. Let’s take a look at the multiples for each of these numbers, 36 and 54: What are the Multiples of 36? What are the Multiples of 54? Let’s take a look at the first 10 multiples for each of these numbers, 36 and 54: First 10 Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360 First 10 Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540 You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 36 and 54 are 108, 216, 324. Because 108 is the smallest, it is the least common multiple. The LCM of 36 and 54 is 108.
LCM of 36 and 54 is the smallest number among all common multiples of 36 and 54. The first few multiples of 36 and 54 are (36, 72, 108, 144, 180, 216, . . . ) and (54, 108, 162, 216, 270, 324, . . . ) respectively. There are 3 commonly used methods to find LCM of 36 and 54 - by prime factorization, by division method, and by listing multiples. What is the LCM of 36 and 54?Answer: LCM of 36 and 54 is 108. Explanation: The LCM of two non-zero integers, x(36) and y(54), is the smallest positive integer m(108) that is divisible by both x(36) and y(54) without any remainder. Methods to Find LCM of 36 and 54The methods to find the LCM of 36 and 54 are explained below.
LCM of 36 and 54 by Prime FactorizationPrime factorization of 36 and 54 is (2 × 2 × 3 × 3) = 22 × 32 and (2 × 3 × 3 × 3) = 21 × 33 respectively. LCM of 36 and 54 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 33 = 108. LCM of 36 and 54 by Listing MultiplesTo calculate the LCM of 36 and 54 by listing out the common multiples, we can follow the given below steps:
∴ The least common multiple of 36 and 54 = 108. LCM of 36 and 54 by Division MethodTo calculate the LCM of 36 and 54 by the division method, we will divide the numbers(36, 54) by their prime factors (preferably common). The product of these divisors gives the LCM of 36 and 54.
The LCM of 36 and 54 is the product of all prime numbers on the left, i.e. LCM(36, 54) by division method = 2 × 2 × 3 × 3 × 3 = 108. ☛ Also Check:
LCM of 36 and 54 Examples
Example 2: Find the smallest number that is divisible by 36 and 54 exactly. Solution: The smallest number that is divisible by 36 and 54 exactly is their LCM.
Therefore, the LCM of 36 and 54 is 108.
Example 3: Verify the relationship between GCF and LCM of 36 and 54. Solution: The relation between GCF and LCM of 36 and 54 is given as, LCM(36, 54) × GCF(36, 54) = Product of 36, 54 Prime factorization of 36 and 54 is given as, 36 = (2 × 2 × 3 × 3) = 22 × 32 and 54 = (2 × 3 × 3 × 3) = 21 × 33 LCM(36, 54) = 108 GCF(36, 54) = 18 LHS = LCM(36, 54) × GCF(36, 54) = 108 × 18 = 1944 RHS = Product of 36, 54 = 36 × 54 = 1944 ⇒ LHS = RHS = 1944Hence, verified. go to slidego to slidego to slide
The LCM of 36 and 54 is 108. To find the LCM of 36 and 54, we need to find the multiples of 36 and 54 (multiples of 36 = 36, 72, 108, 144; multiples of 54 = 54, 108, 162, 216) and choose the smallest multiple that is exactly divisible by 36 and 54, i.e., 108. Which of the following is the LCM of 36 and 54? 108, 35, 21, 27The value of LCM of 36, 54 is the smallest common multiple of 36 and 54. The number satisfying the given condition is 108. What is the Relation Between GCF and LCM of 36, 54?The following equation can be used to express the relation between GCF and LCM of 36 and 54, i.e. GCF × LCM = 36 × 54. If the LCM of 54 and 36 is 108, Find its GCF.LCM(54, 36) × GCF(54, 36) = 54 × 36 Since the LCM of 54 and 36 = 108 ⇒ 108 × GCF(54, 36) = 1944 Therefore, the GCF (greatest common factor) = 1944/108 = 18. What is the Least Perfect Square Divisible by 36 and 54?The least number divisible by 36 and 54 = LCM(36, 54) |