The HCF and LCM of two numbers are 4 and 24 respectively if one of the number is 8 find the other
Selina Solutions Class 6 Mathematics Solutions for Exercise 8(C) in Chapter 8 - HCF and LCM
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Question 3 Exercise 8(C) Next Q3) The H.C.F. and the L.C.M. of two numbers are 50 and 300 respectively. If one of the numbers is 150, find the other one. Answer: Solution 3: H.C.F = 50 L.C.M = 300 Product of L.C.M and H.C.F = 300\times50=15000 One number = 150 The other number = \frac{LCM\times HCF}{One\ number} = \frac{15000}{150}=100 Related Questions Q1) Using the common multiple method, find the L.C.M. of the following :(i) 8, 12 and 24(ii) 10, 15 ... Q2) Find the L.C.M. of each the following groups of numbers, using(i) the prime factor method and(ii... Q4) The product of two numbers is 432 and their L.C.M. is 72. Find their H.C.F. Q5) The product of two numbers is 19,200 and their H.C.F. is 40. Find their L.C.M. Q6) Find the smallest number which, when divided by 12, 15, 18, 24 and 36 leaves no remainder Q7) Find the smallest number which, when increased by one is exactly divisible by 12, 18, 24, 32 and... Was This helpful?
HCF and LCM are the two terms that stand for highest common factor and least common multiple respectively. The HCF is the greatest factor of two numbers or more than two numbers which divides the number exactly with no remainder, while on the contrary the LCM of two numbers or more than two numbers is the smallest number which is divisible by given numbers exactly. After discussing the definition of HCF and LCM, in this article, we will focus on the relation between HCF and LCM along with solved examples and practice questions.
HCF and LCM RelationThe multiplication of common prime factors of given numbers with the least exponential powers is the HCF of two numbers or more numbers. For example, The HCF of 12 and 20 is 4. HCF and LCM of two numbers are related to each other as well as with the given numbers. For any two numbers a and b, HCF (a, b) × LCM (a, b) = a × b. HCF and LCM of Positve IntegersThe product of HCF and LCM of the given positive integers suppose “m” and “n” is equal to the multiplication of the given numbers “m” and “n”. That is, HCF(m,n) × LCM (m,n) =m × n. Let us look at the example based on the above relation. Example: Prove that the LCM (8, 12) × HCF (8, 12) = Product(8, 12) HCF and LCM of Co-Prime numbersLCM of Co-Prime numbers(m, n) = Product of two numbers (m, n). Since the HCF of co-prime numbers is equal to 1, the LCM of two co-prime numbers is the same as the product of the numbers. Look at the given example to verify the relation. For example: 11 and 31 are two co-prime numbers. Let's verify LCM of given co-prime Numbers is equal to the product of the given numbers. HCF and LCM of FractionsTo find HCF and LCM of fractions like m/n, p/q, u/v, etc, we can use the below-mentioned formula: LCM of fractions = LCM of Numerators ÷ HCF of Denominators Let's take two examples to understand it better. Example 1: Find the LCM of the given fractions 1/4, 3/10, 2/5. LCM of fractions = LCM of Numerators ÷ HCF of Denominators Given below is the image to summarize the relation between HCF and LCM. Relation between HCF and LCM of 3 NumbersIn this section, we are going to learn the relation between HCF and LCM of three numbers. Suppose p,q,r are the three numbers, then to find LCM of these three numbers we will multiply the product of numbers (p×q×r) with HCF of numbers(p,q,r) and divide it by the product of HCF(p,q), HCF(q,r) and HCF(r,p). Similarly to find the HCF of p, q, r we will multiply the product of numbers (p×q×r) with LCM of numbers(p,q,r) and divide it by the product of LCM(p,q), LCM(q,r) and LCM(r,p). The below-mentioned formulae can be used to understand the relation and to calculate the HCF and LCM of 3 numbers.
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FAQs on Relation Between HCF and LCMWhat is the Relationship Between HCF and LCM of Two Numbers?The relationship between HCF and LCM of two given positive integers, let's say “m” and “n” is equal to the multiplication of the given numbers “m” and “n”, given as, HCF(m,n) × LCM (m,n) =m × n What is LCM of Two Numbers?The LCM or the least common multiple is the smallest natural number which is a multiple of two or more numbers. For two numbers, we can find the LCM by listing down all the multiples and then selecting the least common multiple of both. Another method is using the prime factorization method. What is the Highest Common Factor?The multiplication of common prime factors of given numbers with the least exponential powers is the highest common factor of two or more numbers. What is the Relation Between HCF and LCM of co-prime numbers?The Relation Between HCF and LCM of co-prime numbers is the product of the numbers = LCM of Co-Prime numbers, as the HCF of co-prime numbers is equal to 1. What are H.C.F. and L.C.M. of Fractions?The HCF and LCM of fractions is given as,
What is the Difference Between LCM and HCF?The LCM of two or more numbers can be divided by the numbers and it is the smallest common multiple of those numbers. The greatest number that divdes the two or more numbers exactly is the highest common factor of those numbers. HCF of two numbers cannot be greater than the numbers, while LCM of two numbers is always greater than or equals to the larger number except 0 which is considered as the common multiple of every number. Can we have two numbers with 24 & 888 as their HCF & LCM respectively?( a whole number) Therefore two numbers can have 888 and 24 as their LCM and HCF respectively.
How do you find two numbers with HCF and LCM?The formula that shows the relationship between their LCM and HCF is: LCM (a,b) × HCF (a,b) = a × b. For example, let us take two numbers 12 and 8. Let us use the formula: LCM (12,8) × HCF (12,8) = 12 × 8. The LCM of 12 and 8 is 24; and the HCF of 12 and 8 is 4.
What pair of numbers have an LCM of 24?It is the least number among the common multiples. Since the least number among 24, 48 and 72 is “24”, the LCM of 8 and 6 is 24.
What is the LCM and HCF of 48 and 60?No. Least Common Multiple of 48 and 60 is 240 and Highest Common Factor of 48 and 60 is 12.
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