1.5 Greatest Common Factor And Least Common Multiple Worksheet With Answers - College Of The Sequoias Page 10

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An interesting result from number theory is the following theorem:
If A and B are two whole numbers, the product of their
LCM and GCF is equal to their product AB.
Verify this theorem for the given pair of numbers.
45. 6 and 8
46. 12 and 16
47. 18 and 27
48. 24 and 30
49. 36 and 60
50. 45 and 60
51. 72 and 144
52. 150 and 300
Answer the following questions (based on the theorem stated above).
53. If two numbers are relatively prime, what does this theorem tell us about their LCM?
54. If the product of two numbers is equal to their LCM, what does this theorem tell us
about the two numbers?
55. Suppose the product of two numbers is 150 and their GCF is 5. What is the LCM of
the two numbers?
56. Suppose the product of two numbers is 144 and their GCF is 4. What is the LCM of
the two numbers?
57. Suppose the product of two numbers is 200 and their LCM is 40. What is the GCF of
the two numbers?
58. Suppose the product of two numbers is 160 and their LCM is 20. What is the GCF of
the two numbers?
59. True or False: The GCF of two numbers is a factor of their LCM.
Explain why/why not.
60. True or False: The LCM of two numbers is a factor of their GCF.
Explain why/why not.
Solve the following application problems.
61. John and Tracy are moving to a new house, and have a lot of books to move. John can
carry 6 books at a time, while Tracy can carry 4. John wants to make 10 trips, then
stop. How many trips will Tracy need to make to have carried the same number of
books?
62. Brad and Ross are sailing to Mexico. Ross can man the helm for 40 minutes before
taking a break, and Brad can man the helm for 25 minutes before breaking. If Ross
takes 10 breaks during their run, how many breaks does Brad take?
63. Three satellites are vertically aligned above the North Pole. One satellite orbits the
earth in 12 hours, another orbits the earth in 15 hours, while the third satellite orbits
the earth in 8 hours. In how long will the satellites again be vertically aligned above
the North Pole?
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