HCF and LCM Questions
Responses:
6. (i) 27
(ii) 4 rose stalks, 3 lily stalks, and 2 orchid stalks
7. After 18 minutes
8. (i) May 7th
(ii) Every 12 days
How can the HCF and LCM be used to find the right responses?
6. The number of stalks of roses = 108
Number of stalks of lilies = 81
Number of stalks of orchids = 54
(i) The largest number of baskets that can be packed is given by the
Highest Common Factor, GCF , or HCF, of 108, 81, and 54, which is
found as follows;
54 = 2 × 27
81 = 3 × 27
108 = 4 × 27
Therefore;
The HCF of 108, 81, and 54 is 27
Which gives;
- The largest number of baskets that can be packed = 27
(ii) From the above factors, we have;
- Number of rose stalks per basket = 4
- Number of lilies per basket = 3
- Number of orchids per basket = 2
7. Length of the circular path = 1 km. = 1,000 m.
Time Lixin takes to walk one round = 18 minutes = 1,080 seconds
Time Khairul takes to run one round = 360 seconds
Time Devi takes to cycle 2 rounds = 4 minutes
Therefore;
Time Devi takes to complete 1 round = [tex]\frac{4}{2}[/tex] = 2 minutes = 120 seconds
Required:
The time at which the three of them will next meet at the starting point
Solution:
The time at which they meet at the starting point is given as the lowest
common multiple, LCM of 1,080, 360, and 120, which is given as
follows.
1,080 = 360 × 3
1,080 = 120 × 9
1,080 = 1,080 × 1
Therefore;
The LCM of 1,080, 360, and 120 is 1,080
- The time they will next meet at the starting point is after 1,080 seconds which is 18 minutes
8. The days off of Nora = Every 4 days
Days off for Amirah = Every 6 days
Nora's last day of = 29 April
Amirah's last day off = 1 May
(i) The next time they will both have the same day off is given as follows;
6·x = 2 + 4·x
2·x = 2
x = 1
Therefore, the next time Amirah has a day off, which is 1 May + 6 days = 7 May, they will both have the same day off.
- They will both have the same day off on May 7
(ii) The number of days that it will take for them to have the same day off is given by the HCF of 4 and 6, which is every 12 days.
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