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CHAPTER 9: Number: Number properties
PS
C
1001 = 7 × 11 × 13
10012 = 1 002 001
10013 = 1 003 003 001
FM
a
Write 1 002 001 as a product of prime factors, in index form.
b
Write 1 003 003 001 as a product of prime factors, in index form.
c
Write 100 110 as a product of prime factors, in index form.
Harriet wants to share £40 between three of her grandchildren. Explain why it is not
possible for them to get equal shares.
Least common multiple
The least common multiple (or lowest common multiple), or LCM of two numbers is the
smallest number that appears in the multiplication tables of both numbers.
For example, the LCM of 3 and 5 is 15, the LCM of 2 and 7 is 14 and the LCM of 6 and 9 is 18.
There are two ways of working out the LCM.
EXAMPLE 9
Find the LCM of 18 and 24.
Write out the 18 times table:
18, 36, 54, 72 , 90, 108, …
Write out the 24 times table:
24, 48, 72 , 96, 120, …
Numbers that appear in both tables are common multiples. You can see that 72 is
the smallest (least) number that appears in both tables, so it is the least common
multiple.
EXAMPLE 10
Find the LCM of 42 and 63.
Write 42 in prime factor form:
42 = 2 × 3 × 7
Write 63 in prime factor form:
63 = 32 × 7
Write down the smallest number, in prime factor form (that includes all the prime
factors of both 42 and 63).
2 × 32 × 7
(This includes 2 × 3 × 7 and 32 × 7.)
Then work it out:
2 × 32 × 7 = 2 × 9 × 7 = 18 × 7 = 126
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