Highest common factor HCF and lowest common multiple LCM. - One Line Questions

1. What is the HCF of any two consecutive integers? — 1
2. Find the HCF of 1.2 and 1.8. — 0.6
3. Find the LCM of 0.5 and 0.25. — 0.5
4. Find the HCF of 17 and 23 (both are prime numbers). — 1
5. Find the LCM of 17 and 23 (both are prime numbers). — 391
6. What is the HCF of a number and itself? — The number itself
7. What is the LCM of a number and itself? — The number itself
8. What is the HCF of 1001 and 1010? — 1
9. What is the HCF of 3/4 and 5/6? — 1/12
10. What is the HCF of 100, 120, and 140? — 20
11. Find the smallest 5-digit number exactly divisible by 12, 15, 18, and 20. — 10800
12. What is the LCM of 1001 and 1010? — 1011010
13. Find the LCM of 108, 120, and 132. — 7920
14. Using prime factorization, find the LCM of 48 and 60. — 240
15. Find the LCM of 36 and 84. — 252
16. Find the HCF of 144 and 192. — 48
17. Find the LCM of 24, 36, and 60. — 360
18. Find the smallest number that is divisible by 25, 30, and 40. — 600
19. Find the smallest number which when divided by 6, 7, and 8 leaves remainders 3, 4, and 5 respectively. — 177
20. Find the LCM of 15, 25, and 35. — 525
21. Find the LCM of 144 and 192. — 576
22. Find the HCF of 12 and 18. — 6
23. What is the HCF of 2^3 * 3^2 * 5 and 2^2 * 3^3 * 7? — 2^2 * 3^2
24. What is the LCM of 2^3 * 3^2 * 5 and 2^2 * 3^3 * 7? — 2^3 * 3^3 * 5 * 7
25. The HCF of two numbers is 8. Which of the following cannot be their LCM? — 60
26. The HCF of two numbers is 11 and their LCM is 7700. If one number is 275, find the other number. — 308
27. Find the largest number that divides 45, 60, and 75 without leaving a remainder. — 15
28. If the HCF of two numbers is 15 and their LCM is 450, and one of the numbers is 75, what is the other number? — 90
29. The product of two numbers is 4107. If their HCF is 37, find their LCM. — 111
30. Using prime factorization, find the HCF of 48 and 60. — 12
31. Find the HCF of 24, 36, and 60. — 12
32. What is the HCF of 16 and 24? — 8
33. Find the LCM of 12 and 18. — 36
34. Find the HCF of 54 and 90 using the Euclidean Algorithm. — 18
35. Find the HCF of 36 and 84. — 12
36. Find the HCF of 108, 120, and 132. — 12
37. Three bells toll at intervals of 12, 15, and 18 minutes respectively. If they start tolling together, after what time will they next toll together? — 180 minutes
38. What is the LCM of 16 and 24? — 48
39. What is the LCM of 2/3 and 4/5? — 4/3
40. The product of two numbers is 960 and their HCF is 10. What is their LCM? — 96
41. Find the greatest 4-digit number exactly divisible by 6, 8, 12, and 16. — 9984
42. If HCF(a, b) = x, then 'x' must be a factor of: — a and b
43. If LCM(a, b) = y, then 'y' must be a multiple of: — a and b
44. If the HCF of two numbers is 1, the numbers are called: — Coprime or relatively prime numbers
45. What is the relationship between the HCF and LCM of two positive integers 'a' and 'b'? — HCF(a, b) * LCM(a, b) = a * b
46. If the prime factorization of a number 'a' is p1^x1 * p2^x2 and the prime factorization of a number 'b' is p1^y1 * p2^y2, how is the HCF calculated using prime factorization? — p1^(min(x1,y1)) * p2^(min(x2,y2))
47. Which method is commonly used to find the HCF of larger numbers by repeatedly applying the division algorithm? — Euclidean Algorithm
48. What is the LCM of any two consecutive integers? — The product of the two integers
49. What is the HCF of three numbers a, b, and c? — The product of the common prime factors raised to the lowest power.
50. What is the LCM of three numbers a, b, and c? — The product of all prime factors raised to the highest power.
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