HCF and LCM: 25 flashcards
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1. What does HCF stand for?
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Highest Common Factor
2. What does LCM stand for?
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Lowest Common Multiple
3. Define HCF in one sentence.
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The largest number that divides two or more given numbers exactly.
4. Define LCM in one sentence.
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The smallest number that is a multiple of two or more given numbers.
5. Find the HCF of 12 and 18.
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$6$
6. Find the LCM of 12 and 18.
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$36$
7. Prime factorisation rule for HCF?
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Take shared primes at their lowest powers.
8. Prime factorisation rule for LCM?
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Take all primes at their highest powers.
9. For $24 = 2^3 \times 3$ and $36 = 2^2 \times 3^2$, what is the HCF?
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$12$
10. For $24 = 2^3 \times 3$ and $36 = 2^2 \times 3^2$, what is the LCM?
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$72$
11. State the product rule linking HCF and LCM for two numbers $a$ and $b$.
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$\text{HCF}(a,b) \times \text{LCM}(a,b) = a \times b$
12. Does the product rule hold for three numbers?
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No — it holds only for two numbers.
13. What is the largest possible value of the HCF of two numbers?
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It is never greater than the smaller of the two numbers.
14. What is the smallest possible value of the LCM of two numbers?
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It is never less than the larger of the two numbers.
15. If two numbers are coprime, what are their HCF and LCM?
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HCF $= 1$ and LCM $=$ their product.
16. Describe the Euclidean algorithm for HCF.
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Repeatedly replace $(a, b)$ with $(b, r)$ where $r$ is the remainder of $a \div b$; stop when $r = 0$; the last non-zero remainder is the HCF.
17. Use the Euclidean algorithm to find HCF(48, 18).
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$6$
18. Which is used to simplify a fraction — HCF or LCM?
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HCF of numerator and denominator.
19. Which is used to find a common denominator when adding fractions?
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LCM of the denominators.
20. Real-world use of HCF?
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Splitting quantities into the largest possible equal groups.
21. Real-world use of LCM?
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Finding when two repeating events next occur together.
22. If the HCF of two numbers is large, what happens to their LCM?
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It becomes small, because their product is fixed.
23. Does the HCF of two numbers always divide their LCM exactly?
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Yes, always.
24. Reliable method to find the HCF of small numbers?
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List all factors of each number and pick the largest common one.
25. Reliable method to find the LCM of small numbers?
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List multiples of each number and pick the smallest common one.
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