GCF and LCM
word problems

In solving gcf and lcm word problems , you use the following rules.

GCF (HCF) LCM
Maximum
Greatest
biggest
largest		 Minimum
least
lowest
Smallest
simultaneously
altogether
If the above words are there in the word problems then according to that words find GCF or LCM.

Examples on GCF and LCM word problems

Example : 1 Two tankers contain 825 liters and 675 liters of kerosene oil respectively. Find the maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times.
Solution : The maximum capacity of the required container has to measure both the tankers in a way that the count is an exact number of times. So its capacity is exactly divisible by both the tankers. Here in the question they have used the word maximum, so we will find the GCF of 825 and 675.

Hence,
825 = 3 x 5 x 5x 11
675 = 3 x 3 x 3 x 5 x 5
The common factor of 825 and 675 is 3,5,5.
Thus the maximum capacity of the required container is 3 x 5 x 5 = 75
Therefore, the first tanker will require 11 seconds to fill it and 2nd tanker will 9 seconds to fill it.
Example 2 : In a morning walk, three persons step off together. Their steps measure 75 cm, 80 cm and 90 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?
Solution : The distance required by each of them is same as well as minimum. The minimum word in the question, that means you have to find the least common multiple (LCM)
So to find the LCM you can use a method of prime factorization.

Thus, the LCM of 75,80 and 90 is = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 = 3600
So the required minimum distance is 3600 cm.
Example 3 : The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?
Solution : The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. As these lights change simultaneously at 7 am. So the minimum time required to change these lights again. As there is a word simultaneously so you have to find the LCM of 48,72 and 108.

Thus, the LCM of 48,72 and 108 = 2 x 2 x 2 x 2 x 3 x 3 x 3= 432 seconds So after 144 seconds = 7 min 12 seconds All the traffic lights will change simultaneously 7 min 12 seconds past 7 am.
GCF and LCM word problems
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