Sat math Essentials

common multiples
of two or more numbers are the multiples that the numbers have in common. The
least common multiple
of two or more numbers is the smallest of all the common multiples. The least common
multiple, or LCM, is used when performing various operations with fractions.
–
N U M B E R S A N D O P E R AT I O N S R E V I E W
–
4 9

---

Examples
Multiples
of 10 include 10, 20, 30, 40, 50, 60, 70, 80, 90 . . .
Multiples
of 15 include 15, 30, 45, 60, 75, 90, 105 . . .
Some 
common multiples
of 10 and 15 are therefore 30, 60, and 90 because they are multiples of both 10 and 15.
The 
least common multiple
of 10 and 15 is therefore 30. It is the smallest of the multiples shared by 10 and 15.
P r i m e a n d C o m p o s i t e N u m b e r s
A positive integer that is greater than the number 1 is either prime or composite, but not both.
■
A 
prime number
has only itself and the number 1 as factors:
2, 3, 5, 7, 11, 13, 17, 19, 23 . . .
■
A 
composite
number is a number that has more than two factors:
4, 6, 8, 9, 10, 12, 14, 15, 16 . . .
■
The number 1 is neither prime nor composite.
Practice Question
n
is a prime number and
n
> 2
What must be true about 
n
?
a.
n
3
b.
n
4
c.
n
is a negative number
d.
n
is an even number
e.
n
is an odd number
Answer
e.
All prime numbers greater than 2 are odd. They cannot be even because all even numbers are divisible
by at least themselves 
and
the number 2, which means they have at least two factors and are therefore
composite, not prime. Thus, answer choices