Transcript Least Common Multiple (LCM)

The smallest
postive number
that is a multiple of
two or more given
STEP 1: List the first 10 multiples of the greater
number.
STEP 2: List the multiples of the lesser number.
Stop when you get to a multiple that was in
your first list.
NOTE: You may find that after listing several
multiples for the lesser number that you still do
not have a common multiple. If this is the case,
Find the least common multiple of 6 and 9
9, 18, 27, 36, 45, 54, 63, 72, 81,
Multiples of 9:
90
_____________________________
6, 12, 18
Multiples of 6:
_____________________________
1
8
Least Common Multiple of 6 and 9: __
Find the least common multiple of 5, 8, and 10.
10, 20, 30, 40, 50, 60, 70, 80, 90,
Multiples of 10:
100
____________________________
8, 16, 24, 32, 40
Multiples
of
8:
Since you have a common multiple for 10 and 8, ask
____________________________
yourself,
“is that number is also a multiple of 5?” If it is
you have the LCM, if not continue to the next common
multiple of 10 and 8.
4
***This will be very similar to how we found
the GCF*** but there is an added twist at the
end
Example 1: Find the
LCM(10,12)
Find the GCF
of the numbers
given
2 10
5
12
6
Multiply each of the numbers circled to find the
LCM.
Example 2: Find the
LCM(15,25)
Find the GCF
of the numbers
given
5 15
3
25
5
Multiply each of the numbers circled to find the
LCM.
5 • 3 • 5 = 75  the LCM of 15 and 25 is 75
Example 3: Find the
LCM(6,8,12)
Find the GCF of the
numbers given
Since two of the
numbers share a
Since
twocontinue
of the
factor…
numbers share a
factor… continue
2 6 8 12
2 3 4 6
33 2 3
1 2 1
Multiply each of the numbers circled to find the
LCM.
IF THE NUMBERS HAVE A
gcF OF 1, THEN THE LCM
IS THE PRODUCT OF ALL
THE NUMBERS
MULTIPLIED
TOGETHER!!!!
Example: LCM(2,5,13):
Rod helped his mom plant a
vegetable garden. Rod
planted a row every 30
minutes, and his mom planted
a row every 20 minutes. If
they started together, how
long will it be before they both
finish a row at the same time?
Least Common Multiple of 30 and 60: __
Three bike riders ride around a
circular path. The first rider
circles the path in 4 minutes,
the second in 9 minutes, and
the third in 12 minutes. If they
all start at the same place at
the same time, and go in the
same direction, after how many
minutes
will
they
meet
at
the
Least Common Multiple of 4, 9, and 12: __