LCM of 18 and 40 is the smallest number among all common multiples of 18 and 40. The first few multiples of 18 and 40 are (18, 36, 54, 72, 90, 108, 126, . . . ) and (40, 80, 120, 160, 200, . . . ) respectively. There are 3 commonly used methods to find LCM of 18 and 40 - by division method, by listing multiples, and by prime factorization. Show
What is the LCM of 18 and 40?Answer: LCM of 18 and 40 is 360. Explanation: The LCM of two non-zero integers, x(18) and y(40), is the smallest positive integer m(360) that is divisible by both x(18) and y(40) without any remainder. Methods to Find LCM of 18 and 40The methods to find the LCM of 18 and 40 are explained below.
LCM of 18 and 40 by Listing MultiplesTo calculate the LCM of 18 and 40 by listing out the common multiples, we can follow the given below steps:
∴ The least common multiple of 18 and 40 = 360. LCM of 18 and 40 by Prime FactorizationPrime factorization of 18 and 40 is (2 × 3 × 3) = 21 × 32 and (2 × 2 × 2 × 5) = 23 × 51 respectively. LCM of 18 and 40 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 32 × 51 = 360. LCM of 18 and 40 by Division MethodTo calculate the LCM of 18 and 40 by the division method, we will divide the numbers(18, 40) by their prime factors (preferably common). The product of these divisors gives the LCM of 18 and 40.
The LCM of 18 and 40 is the product of all prime numbers on the left, i.e. LCM(18, 40) by division method = 2 × 2 × 2 × 3 × 3 × 5 = 360. ☛ Also Check:
LCM of 18 and 40 Examples
Example 2: The product of two numbers is 720. If their GCD is 2, what is their LCM? Solution: Given: GCD = 2 product of numbers = 720 ∵ LCM × GCD = product of numbers ⇒ LCM = Product/GCD = 720/2 Therefore, the LCM is 360. The probable combination for the given case is LCM(18, 40) = 360.
Example 3: Find the smallest number that is divisible by 18 and 40 exactly. Solution: The value of LCM(18, 40) will be the smallest number that is exactly divisible by 18 and 40.
Therefore, the LCM of 18 and 40 is 360. go to slidego to slidego to slide
The LCM of 18 and 40 is 360. To find the least common multiple (LCM) of 18 and 40, we need to find the multiples of 18 and 40 (multiples of 18 = 18, 36, 54, 72 . . . . 360; multiples of 40 = 40, 80, 120, 160 . . . . 360) and choose the smallest multiple that is exactly divisible by 18 and 40, i.e., 360. What are the Methods to Find LCM of 18 and 40?The commonly used methods to find the LCM of 18 and 40 are:
What is the Relation Between GCF and LCM of 18, 40?The following equation can be used to express the relation between GCF and LCM of 18 and 40, i.e. GCF × LCM = 18 × 40. What is the Least Perfect Square Divisible by 18 and 40?The least number divisible by 18 and 40 = LCM(18, 40) If the LCM of 40 and 18 is 360, Find its GCF.LCM(40, 18) × GCF(40, 18) = 40 × 18 Since the LCM of 40 and 18 = 360 ⇒ 360 × GCF(40, 18) = 720 Therefore, the GCF (greatest common factor) = 720/360 = 2.
The Highest Common Factor (HCF) of two numbers is the highest possible number which divides both the numbers completely. The highest common factor (HCF) is also called the greatest common divisor (GCD). There are many ways to find the HCF of two numbers. One of the quickest ways to find the HCF of two or more numbers is by using the prime factorization method. Explore the world of HCF by going through its various aspects and properties. Find answers to questions like what is the highest common factor for a group of numbers, easy ways to calculate HCF, its relation with LCM, and discover more interesting facts around them. HCF DefinitionThe HCF (Highest Common Factor) of two or more numbers is the highest number among all the common factors of the given numbers. In simple words, the HCF (Highest Common Factor) of two natural numbers x and y is the largest possible number that divides both x and y. Let us understand this definition using two numbers, 18 and 27. The common factors of 18 and 27 are 1, 3, and 9. Among these numbers, 9 is the highest (largest) number. So, the HCF of 18 and 27 is 9. This is written as: HCF (18,27) = 9. Observe the following figure to understand this concept. HCF ExamplesUsing the above definition, the HCF of a few set of numbers can be listed as follows:
How to Find HCF?There are many ways to find the highest common factor of the given numbers. Irrespective of the method, the answer to the HCF of the numbers would always be the same. There are 3 methods to calculate the HCF of two numbers:
Let us discuss each method in detail with the help of examples. HCF by Listing Factors MethodIn this method, we list the factors of each number and find the common factors of those numbers. Then, among the common factors, we determine the highest common factor. Let us understand this method using an example. Example: Find the HCF of 30 and 42. Solution: We will list the factors of 30 and 42. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30 and the factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. Clearly, 1, 2, 3, and 6 are the common factors of 30 and 42. But 6 is the greatest of all the common factors. Hence, the HCF of 30 and 42 is 6. HCF by Prime FactorizationIn order to find the HCF of numbers by the prime factorization method, we use the following steps. Let us understand this method using the example given below.
Example: Find the HCF of 60 and 90. Solution: The prime factors of 60 = 2 × 2 × 3 × 5; and the prime factors of 90 = 2 × 3 × 3 × 5. Now, the HCF of 60 and 90 will be the product of the common prime factors, which are, 2, 3, and 5. So, HCF of 60 and 90 = 2 × 3 × 5 = 30 HCF by Division MethodThe HCF of two numbers can be calculated using the division method. Let us understand this using the following steps and the example given below.
Example: Find the HCF of 198 and 360 using the division method. Solution: Among the two given numbers, 360 is the larger number, and 198 is the smaller number. We divide 360 by 198 and check the remainder. Here, the remainder is 162. Make the remainder 162 as the new divisor and the previous divisor 198 as the new dividend and perform the long division again. We will continue this process till we get the remainder as 0. Here, the last divisor is 18 which is the HCF of 198 and 360.
HCF of Multiple NumbersThe method to find the HCF of multiple numbers is the same when we use the 'listing factors method' and 'the prime factorization method'. However, while using the division method, there is a slight change in the case of multiple numbers. Let us learn how to find the HCF of three numbers using the division method. HCF of Three NumbersIn order to find the HCF of three numbers, we use the following procedure. Let us understand this using the steps and the example given below.
Example: Find the HCF of 126, 162, and 180. Solution: First, we will find the HCF of the two numbers 126 and 180. The HCF of 126 and 180 = 18. Then, we will find the HCF of the third number, which is 162, and the HCF of the two numbers obtained in the previous step, that is, 18. This will give the final HCF of all the three numbers.
Therefore, HCF of 126, 162 and 180 = 18 HCF of four numbersTo find the HCF of four numbers, we use the following steps.
HCF of Prime NumbersWe know that a prime number has only two factors, 1 and the number itself. Let us consider two prime numbers 2 and 7, and find their HCF by listing their factors. The factors of 2 = 1, 2; and the factors of 7 = 1, 7. We can see that the only common factor of 2 and 7 is 1. Hence, the HCF of prime numbers is always equal to 1. Properties of HCFWe already know that the HCF of a and b is the highest common factor of the numbers a and b. Let us have a look at the important properties of HCF: The properties of HCF are given below.
Relation Between LCM and HCFThe HCF of two or more numbers is the highest common factor of the given numbers. It is found by multiplying the common prime factors of the given numbers. Whereas the Least Common Multiple (LCM) of two or more numbers is the smallest number among all common multiples of the given numbers. LCM (a,b) × HCF (a,b) = a × b Let us understand this relationship with an example. Example: Let us find the HCF and LCM of 6 and 8 to understand their relationship. Solution: The HCF of 6 and 8 = 2; The LCM of 6 and 8 = 24; The product of the two given numbers is 6 × 8 = 48. So, let us substitute these values in the formula that explains the relationship between the LCM and HCF of two numbers. On substituting the values in the formula, LCM (a,b) × HCF (a,b) = a × b, we get, 24 × 2 = 48. ☛ Related Articles
FAQs on HCFThe HCF (Highest Common Factor) of two numbers is the highest number among all the common factors of the given numbers. For example, the HCF of 12 and 36 is 12 because 12 is the highest common factor of 12 and 36. How to find the Highest Common Factor (HCF)?There are 3 methods to calculate the HCF of two numbers:
These methods are explained in detail with examples under the section How to find HCF? on this page. What are the Properties of HCF?The properties of HCF are listed as follows:
How to find HCF by Division Method?The steps to find the HCF of two numbers using long division are mentioned below:
What is the Difference Between HCF and LCM?The Least Common Multiple (LCM) of two or more numbers is the smallest number among all the common multiples of the given numbers and the HCF (Highest Common Factor) of two or more numbers is the highest number among all the common factors of the given numbers. What is the Relationship between HCF and LCM of two Numbers?The formula that expresses the relationship between the Least Common Multiple (LCM) and HCF is given as, LCM (a,b) × HCF (a,b) = a × b; where 'a' and 'b' are the two numbers. What is the HCF of two Consecutive Natural Numbers?The HCF of two consecutive natural numbers is 1. This is due to the fact that there is no common factor between any two consecutive numbers other than 1. Therefore, 1 is always is the HCF between two consecutive numbers. What is the HCF of two Co-prime Numbers?Co-prime numbers are those numbers whose common factor is only 1. For example, (4 and 7) and (8 and 15) are co-prime numbers. Since Co-prime numbers have only 1 as their highest common factor, their HCF is always 1. What is the HCF of two Consecutive Even Numbers?The HCF of two consecutive even numbers is always 2. We know that the HCF (Highest Common Factor) of two or more numbers is the highest number among all the common factors of the given set of numbers. For example, the HCF of 6 and 8 is 2, the HCF of 14 and 16 is also 2. How to Find the HCF of 3 Numbers?To find the HCF of three numbers, we use the following steps. Let us find the HCF of 4, 6, and 8 to understand the steps.
How to find HCF by Prime Factorization?In order to find the HCF of numbers by prime factorization, we use the following steps. For example, let us find the HCF of 24 and 36.
Why is HCF Important?HCF is important because it is used to split something into small sections, to distribute items to larger groups, or to arrange something into groups. |