Can anybody give me a Least Common Multiple problem that we will use in real life?

Answer 1

PROBLEM 1:
The hot dog marketers, in their infinite wisdom have decided to sell hot dogs 8 to a pack. However buns are sold 12 to a pack. What's the smallest number of each would you need to not have leftovers of either?

LCM(8, 12) = 24

So you need to buy 24 hot dogs (3 packs) and 24 buns (2 packs) to not have leftovers.

PROBLEM 2:
Joe has custody of his children and sees them once a week on Sundays. His girlfriend Sally gets to see her children every third day. Also, their favorite thing to do is go to a movie, but the budget theater only opens every other day. If they just took all the kids to the movies today, when is the next time they can do this again?

LCM(7, 3, 2) = 42

So they can do this again in 6 weeks (42 days).

PROBLEM 3:
Ten children will be coming to the easter egg hunt. I want everyone to get the same number of eggs which are sold by the dozen. What's the smallest number of eggs I need to buy so everyone gets the same number with no leftovers?

LCM(10, 12) = 60

So I must buy 60 eggs (5 dozen) so everyone is happy.

Answer 2

Sort of applicable: The planets align themselves at this date. If Planet X completes a revolution in x amount of time, and Planet Y in y amount of time, when is the next time they will be together?
Answer: The least common multiple of the two times, BUT you need to consider the original starting time in your answer.


A box fits ten dolls. I want to get enough dolls to fill however many boxes I need to fill them completely, but the dolls come in packs of 12. How many boxes and dolls do I need?
Answer: 10=2*5; 12=2^2*3
2^2*5*3 = 60, which is divisible by 10 and 12.


I love books. However, I am very precise about how many books I have. I must have the same number of sci-fi books as romance novels. If romance novels are sold in packs of 7 and sci-fi novels in packs of 11, how many sci-fi and romance novel packs do I need? How many books of each?
Answer: 77, since 11 and 7 are both prime.


I operate a theater. There is a problem with the lights, they have started going on and off at regular intervals. One of them seems to go off every 11 minutes, the other every 21 minutes. If I can catch them both on at the same time and flip off the power, I'll fix the problem. They are both on now at 12 midnight and I missed it. When is my next chance?
Answer: 3*7*11=231 minutes from now, which is 3 hours (180 minutes) and 51 minutes from now, so at 3:51

I am a military strategist. The enemy has patrols that circle their camp every so often. One completes a round every 9 days, the other every 16 days. I was planning to ambush both of them at the same time when they are together. If they are together now (when I thought of the plan), in how many days will I be able to launch a successful attack?
Answer: 3^2*2^4=6*6*4=24*6=144 days.


Hope this helps.

Answer 3

say, three bells rang together and then they continued ringing after 12 sec,20 sec and 30 sec respectively.
after how many seconds did they ring together again?

this is a real life problem of LCM.

the first bell rang after 12, 24, 36, 48, 60 ,72......sec.
the second bell rang after 20, 40, 60,80.......sec
the third bell rang after 30, 60, 90......sec.

so they would ring together again after 60 sec...which is the LCM of 12,20, 30.

got it?