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MULTIPLES AND
LEAST COMMON MULTIPLES
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Multiple
• The product of a whole number multiplied times any other whole number.
Some multiples of 6 6, 12, 18, 24, 30, 36, 42…
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Name some multiples of 5
5, 10, 15, 20, 25, 30, 35….
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Name some multiples of 7
7, 14, 21, 28, 35, 42, 49….
3
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Name some multiples of 4
4, 8, 12, 16, 20, 24, 28…•
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Name some multiples of 9
9, 18, 27, 36, 45, 54, 63…..
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Common Multiple
• A number that is a multiple of two or more numbers.
6 and 86-- 6, 12, 18, 24, 30, 36,
42,48,54,60..8– 8,16,24,
32,40,48,56,64,72,80…..
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What is the Least Common Multiple of 6 & 8
• 6 = 6, 12, 18, 24, 30, 36,42,48,54,60..
• 8 = 8, 16,24,32,40,48,56,64,72,80…
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What is the Least Common Multiple of 3 & 9
3 = 3, 6, 9, 12, 15, 21, 24,27,30,33…
9 = 9, 18, 27, 36, 45, 54,63,72,81,90…
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The Ladder Method(SLED)
For Finding LCD, GCF,
distributive property and
Simplifying Fractions
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The Ladder Method (SLED)
is a method of factoring which allows you to factor two numbers at once
in order to…• find the LCM of the two numbers• find the GCF of the two numbers• simplify a fraction with these numbers as
numerator and denominator• Finding distributive property
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Use the ladder to factor6 and 8
You will divide out any common factors of the two numbers
What number goesinto both 6 and 8?
Now divide both6 and 8 by the 2
Does any # besides 1go into both 3 and 4?
No? Then you are done.ONE YOUR DONE!
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Let’s find the Least Common Multiple (LCM) of
6 and 8The LCM is the product of all the
numbers on the left and the bottom.
The LCMof
6 and 8is 24.
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Which numbers in the ladder give you the LCM?
The “L” shape gives you the LCM: multiply the numbers
on the left and bottom.
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Let’s try some bigger numbers.
Divide out all the common factors down the left side.
What numbergoes into both
24 and 60?Does any #
besides 1go into both 12 and 30?How about6 and 15?
Anything else?No?
You’re done.ONE YOUR DONE
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x
x
xx
Find the LCM.
=120
The LCMof
24 and 60is 120.
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G.C.F. is to the left
L.C.M. is all of them
Becky Afghani, LBUSD Math Curriculum Office, 2003
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Practice. Find the LCM and Practice. Find the LCM and
GCF for 28 and 42. GCF for 28 and 42.
LCM = 2 7 2 3 = 84
GCF = 2 7 = 14