Download ROD: Lowest Common Multiple

ROD: Lowest Common Multiple
______________
A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3
and 4 are 0, 12, 24, ....
The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of
both. It can be used to find the lowest common denominator when adding, subtracting or comparing
fractions
Eg.1: Find the LCM of 3 and 4:
Don't let the "least" in the name fool you - the LCM is no smaller than the largest
of the numbers.
HINTS:
LEAST - lowest or smallest.
COMMON - something shared or in common.
MULTIPLE - what you get when you multiply.
Eg.2:
Find the Least Common Multiple (L.C.M.) of 4 and 6.
Multiples of 4:
4,
8, 12, 16, 20, 24, 28, 32....
1*4, 2*4, 3*4, 4*4, 5*4, 6*4, and so on
Multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48....
1*6, 2*6, 3*6, 4*6, 5*6, 6*6, and so on
Since 12, 24, 36, 48.... can be all divided by BOTH 4 and 6, each of them is a
common multiple. The lowest common multiple is 12, therefore it is the Least
Common Multiple (L.C.M.) of 4 and 6.
Math Model Book: Comparing Fractions
____________
How can we compare fractions with the same numerator?
e.g. ½ , ¼
The larger the denominator, the smaller the fraction.
How can we compare fractions with the same denominator?
The larger the numerator, the larger the fraction.
2
5 is
1
larger than 5 .
How can we compare fractions when the numerators and
denominators are different?
Change them to equivalent fractions with the same denominator.
Then, compare the numerators.
Example 8. Which is larger,
1
2
or
3
8?
Answer. Make a common denominator. Choose the LCM of 2
and 8 -- which is 8 itself.
We will change
1
2
=
4
8
1
2
to an equivalent fraction with denominator 8:
.
The denominators are now the same, and we can
compare
We see:
4
8
is larger than 8 .
3
1
2
is larger than
That is,
3
8
4
3
with
.
8
8
Proper and Improper Fractions _______
Proper and Improper fractions
2 ½ is read two and one-half
This means 2 + ½ or
4 + ½ or
2
5
2
2½
Whole #
And a fraction
mixed number
5/2
improper
fraction
e.g 1 Convert 5/4 to a proper fraction:
e.g 2 Convert 2 ¾ to an improper fraction
numerator greater than
denominator
Math Model Book: Reducing Fractions
___________________
To reduce fractions to its lowest terms, we divide the numerator and the denominator by
their GCF
e.g. Reduce 20/25
divide top and bottom by 5 to get ____________________
In other words, we find an equivalent fraction by dividing by a form of one
12 12 4 3
=
÷ =
16 16 4 4
A form of 1 = 4/4