Page 15 - Math Smart - 7

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Sam used the factors of 32 and 48 to work out the length of the pieces she should cut.
Factors of 32 are 1, 2, 4, 8, 32
Factors of 48 are 1, 2, 3, 4, 6, 8, 12,1£ 24, 48
Common factors are 1, 2, 4, 8, 16. The highest factor is 16.

The highest common factor of the numbers 32 and 48 is 16.
32 cm 48 cm

16 cm 16 cm 16 cm 16 cm 16 cm
► Figure 1.2 Sam cut
them into widths of
16 cm

1.2.1 Lowest Common Multiple (LCM) Multiples that are

common to two or more
Example 3 numbers are called
common multiples. The
Kit and Tina are running on a circular track. They start from the same point but numbers 90 and 180 are
Kit takes 30 seconds to run a lap while Tina takes 45 seconds to run a lap. After both common multiples
how many seconds will they meet again at the starting point? of 30 and 45. The number
90 is the lowest common
Answer
multiple of 30 and 45.
We can list the multiples of 30 and 45 to help us;
Multiples of 30 are 30, 60, 90, 120, 150, 180, 210, 240, 270...
Multiples of 45 are 45, 90, 135, 180, 225, 270....

90 is the first multiple that occurs in both lists. We say that 90 is the Lowest Check My
Common Multiple (LCM) of 30 and 45. Kit and Fandi will meet at the start line
again after 90 seconds. They will meet again after 180 seconds. Understanding

Example 4 O Find the lowest common
multiple of:
O Find the first three common muitiples of 6 and 8. a) 5 and 7
© What is the LCM of 6 and 8? b) 6and 15
c) 4 and 6
Answer
d) 7 and 14
The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72...
e) 11 and 12
The multiples of Bare: 8, 16, 24, 32, 40, 48, 56, 64, 72...
f) 20 and 36
O The first three common multiples of 6 and 8 are 24, 48 and 72. The g) 15 and 50
numbers 24, 48 and 72 occur in both lists of multiples. h) 18 and 24
O The LCM of 6 and 8 is 24. The number 24 is the smallest number that
occurs in both lists of multiples.