Quick Guide For HCF & LCM
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What is HCF? What is LCM? How you calculate HCF & LCM of numbers & fractions quickly? Find out in this short presentation by https://allexammocktest.in
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This document discusses highest common factors (HCF) and least common multiples (LCM). It provides examples of calculating HCF and LCM using prime factorization and division methods for numbers, polynomials, and fractions. The key points are:
- HCF is the greatest number that divides two or more numbers. LCM is the smallest number divisible by two or more numbers.
- Prime factorization and division methods can be used to calculate HCF and LCM of numbers.
- For polynomials, the product of common factors is the HCF and the product of factors with highest powers is the LCM.
- For fractions, the HCF is the HCF of numerators and LCM of denomin
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Quick Guide For HCF & LCM
- 1. What is HCF & LCM ? HCF (Highest Common Factor) - The HCF of 2 numbers is the largest common factor that they have. LCM (Lowest Common Multiple) – The LCM of 2 numbers is the smallest common factor they they have.
- 2. Example - 12,20 and 30 See there are only two common factors 1 and 2. 2 is the largest common factor. Similarly, 60 is the smallest common multiple. So, The answer is - 2 is the HCF and 60 is the LCM.
- 3. Tricks to Find Out HCF & LCM Quickly We shall find out the HCF and LCM of 18, 27 and 30 in 3 quick steps. Step-1 1. Start by factorizing all three numbers in terms of prime factors So now there are 3 prime factors - 2, 3 and 5.
- 4. Step-2 Now we are going to express the above 3 equations in such a way that all 3 of them contains 2, 3 and 5. Look closely –
- 5. Step 3 In this last step we shall find both the HCF and LCM – ● For HCF, we take the smallest power of 2, 3 and 5 that is common in the 3 equations and multiply them. ● For LCM, we take the largest power of 2, 3 and 5 in the 3 equations and multiply them. [Please note that this power does not have to be common]
- 6. Practice Problems Find the HCF and LCM of the following numbers using the method above. (Try to solve them as fast as you can.) – 1) 12, 28 and 44 2) 132, 246 and 444 3) 121, 605 and 12321
- 7. HCF and LCM of Fractions ● The formula for finding the HCF of fractions is – ● The formula for finding the LCM of fractions is –
- 8. The Easy Way To Remember The Formula The numerators do what you have to do. The denominators do opposite of what you have to do. If you need to do HCF, then with the numerators of the fractions find the HCF. Then, find the LCM with the denominators. Finally form the fraction. To find the LCM, find the LCM of the numerators. Next, find the HCF of the denominators. Then form the fraction.
- 9. Solve Example With This Formula –
- 10. Solve Other Example -
- 11. Practise Set - Find the HCF & LCM of the following Example
- 12. Another Important Formula If M and N are two numbers. And X and Y are the HCF and LCM of M and N, then – M x N = X x Y That means, The product of two numbers = HCF x LCM
- 13. Example Find the smallest such number, which is greater than 3 and when divided by 4, 5, 6 always leaves the same remainder 3. Solution – This problem can be solved in 2 steps – 1. Find the smallest number that is divisible by 4, 5, 6. Obviously, the smallest such number is their LCM = LCM (4, 5, 6) = 60. 2. Add 3 to that number to get the required answer. Therefore the answer is = 60 + 3 = 63.
- 14. Want To Solve More Questions ? Visit our website - www.allexammocktest.in/exams