Applications for LCMs

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Applications for LCMs
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Work on this problem

• Juan, Sean and Jane are night guards at an
  industrial complex. Each starts work at the
  central gate at 12 midnight. Each guard spends
  the night repeating a round which starts and ends
  at the gate. Juans round takes 30 minutes
  Seans round takes 40 minutes and Janes round
  takes 80 minutes. If they all head out from the
  gate at midnight, what is the next time that
  they will all be at the gate.

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Juan, will return at 1230, 100, 130 and so
forth.
Sean, will return at 1240, 120, 200 and so
forth.
Jane, will return at 120, 240, 420 and so
forth.
Working with times can be awkward. It is best to
work with minutes.
Juan, will return after 30 minutes, 60 minutes,
90 minutes, and so forth.
Sean, will return after 40 minutes, 80 minutes,
120 minutes, and so forth.
Jane, will return after 80 minutes, 160 minutes,
240 minutes, and so forth.
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You should recognize this as an application of
the Least Common Multiple.
Juan 30, 60, 90, 120, 150, 180, 210, 240, 270,
300,
Sean 40, 80, 120, 160, 200, 240, 280, 320,
Jane 80, 160, 240, 320,
After 240 minutes they are all at the gate.
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You can also model the rounds this way.
Juan
Sean
Jane
After four rounds for Juan and three rounds for
Sean, they are both back at the gate. Every time
Jane comes back to the gate, Sean is there. It
is only in 240 minutes, after Juan has made 8
rounds, Sean has made 6 rounds and Jane has made
3 rounds, that all three meet at the gate.
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What have we forgotten?
Juan, Sean and Jane are night guards at an
industrial complex. Each starts work at the
central gate at 12 midnight. Each guard spends
the night repeating a round which starts and ends
at the gate. Juans round takes 30 minutes
Seans round takes 40 minutes and Janes round
takes 80 minutes. If they all head out from the
gate at midnight, what is the next time that
they will all be at the gate.
We know that the guards meet at the gate again
after 240 minutes, however the problem asks for a
time.
240 minutes divided by the 60 minutes in an hour
give us 4 hours.
4 hours after 12 midnight is 4 a.m.
The guards meet at the gate again at 4 a.m.
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Now work on this problem

• You neighbor is putting down a floor with
  rectangular pieces of plywood. Each piece of
  plywood is 6 feet by 8 feet. If the floor is
  square, what is the least possible number of
  plywood pieces used? Draw a diagram of the
  situation and solve.

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Start with one 6 x 8 board and add boards to the
right and below until you have a square. You
will need to click to add boards.
We have our square floor. It is 24 feet by 24
feet. It uses 4 x 3 12 boards. The area of
the floor is 24 x 24 576 square feet.
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Reread the problem to remember what it asked us
to find.
You neighbor is putting down a floor with
rectangular pieces of plywood. Each piece of
plywood is 6 feet by 8 feet. If the floor is
square, what is the least possible number of
plywood pieces used? Draw a diagram of the
situation and solve.
We need to find the minimum number of boards that
will make a square floor 12 boards are needed
to make a square floor.
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Make sure that you work the problems in the
exercises!
Right click and select End Show. Then Close to
return.