Least Common Multiple
The least common multiple (lcm)
of two or more integers is that number all these integers divide.
Procedure:
to find the lcm
1. write each number in their prime factorizations above one another
2. select every factor from each number and use the largest
exponent of each selected factor from all these numbers.
Example:
6, 10
6 = 2 * 3
10 = 2 * 5
lcm
= 2 * 3 * 5 = 30
Example:
20, 30, 50
20 = 22 * 5
30
= 2 * 3 * 5
50 = 2 * 52
lcm
= 22 * 3 * 52
= 300
Example:
8, 15
8 = 23
15
= 3 * 5
lcm
= 23 * 3 * 5 = 120
Word Problems that use
lcm.
Example: You and
your three friends go to lunch and find a deal on packages of 6 tacos.
You want to buy the minimum number of packages so you each get the came number
of tacos and none are left over. How many packages must you buy?
Answer: the lcm of 4 and
6 is
4 = 22
6 = 2 * 3
lcm = 22 * 3 = 12. 12 tacos requires 2
packages and you each will get 3 tacos.
Example: One
trip around a running track is 440 yards. One jogger
can complete one lap in 8 minutes, the other can complete it in 6
minutes. How long will it take for both joggers to arrive at thir
starting point together if they start at the same time and maintain their
jogging pace?
Answer: This is
another lcm problem, so the lcm of 6 and 8 is
6 = 2 * 3
8 = 23
lcm = 23 * 3 = 24 minutes
the slower jogger will hae completed 3 laps ( 3 *
8 = 24 )
while the faster
jogger will have completed 4 laps ( 4 * 6 = 24)
Example:
(advanced) You can make groups of 3, 4, or 9 pencils with none
left over. What is smallest number of pencils you must have to make
these groups?
Answer: lcm of 3,
4, and 9 is
3 = 3
4 = 22
9 = 32
lcm = 22 * 32 = 36 pencils.
(3 groups of 12 pencils, 4
groups of 9 pencils, or 9 groups of 4 pencils)
Back to Integers
Greatest Common Divisor
This is another
FREE ALGEBRA PRINTABLE presented to you from the
Algebra section of
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