Real-life Problem involving LCM:
- A prime number is a whole number that has exactly 2 different factors, 1 and itself.
- A composite number is a whole number that has more than 2 different factors.
- The process of expressing 18 as a product of its prime factors is called the prime factorisation of 18.
- The Lowest Common Multiple (LCM) of two or more numbers is the smallest multiple that is common to all the numbers.
Q. Find the lowest common multiple of 30 and 36.
Solution:
common prime factors
30 = 2 x 3 x 5
36 = 2 x 2 x 3 x 3
________________________
LCM of 30 and 36 = 2 x 2 x 3 x 3 x 5
= 180
Q.1. Three bells toll at regular intervals of 15 minutes, 16 minutes and 36 minutes respectively. Given that they toll together at 2.00 p.m. at what time will they next toll together?
15 = 5 x 3
16 = 4 x 2 x 2
36 = 3 x 3 x 2x 2
LCM of 15, 16 , 36 = 2 x 2 x 3 x 5 x 4 x 3
= 720 minutes
720/60
= 12 hours
Q.2. Farhan has three pieces of rope with lengths of 140 cm, 168 cm and 210 cm. He wishes to cut all the three pieces of ropes into smaller pieces of equal length such that there is no leftover rope.
i) What is the greatest possible length of each of the smaller pieces of rope?
ii) How many smaller pieces of rope can he get altogether?
Q.13. The lights on three lightships flash at regular intervals. The first light flashes every 18 seconds, the second every 30 seconds and the third every 40 seconds. The three lights flash together at 10.00 p.m. At what time will they next flash together?
18 = 2 x 3 x 3
30 = 2 x 3 x 5
40 = 2 x 2 x 5
LCM of 18, 30 and 40 = 2 x 2 x 2 x 3 x 3 x 5
= 360
360 seconds = 6 minutes
The three lights will next flash together at 10.06 p.m.
Q.7. Huixian needs to pack 171 pens, 63 pencils and 27 erasers into identical gift bags so that each item is equally distributed among the gift bags. Find
i) the largest number of gift bags that can be packed
ii) the number of each item in a gift bag.
Q. 6. Shirley needs to pack 108 stalks of roses, 81 stalks of lilies and 54 stalks of orchids into identical baskets so that each type of flowers is equally distributed among the baskets. Find
i) the largest number of baskets that can be packed
ii) the number of each type of flowers in a basket