8 Assumed Knowledge (Number)Thelowest common multipleorLCMof two or more positive integers is the smallest multiple
which is common to all of them.Example 11 Self Tutor
Find the LCM of: a 3 and 4 b 3 , 4 and 8a The multiples of 3 are: 3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 , 27 , ......
The multiples of 4 are: 4 , 8 , 12 , 16 , 20 , 24 , 28 , 32 , ......
) the common multiples of 3 and 4 are: 12 , 24 , 36 , ...... of which 12 is the LCM.
b The multiples of 3 are: 3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 , 27 , ......
The multiples of 4 are: 4 , 8 , 12 , 16 , 20 , 24 , 28 , 32 , ......
The multiples of 8 are: 8 , 16 , 24 , 32 , 40 , ......
So, the LCM is 24.1 List all the factors of:
a 10 b 16 c 18 d 17
e 36 f 42 g 64 h 1002 List the firstfivemultiples of:
a 6 b 11 c 13 d 293 Find the HCF of:
a 3 , 12 b 8 , 12 c 18 , 24 d 13 , 52
e 3 , 5 , 6 f 15 , 20 , 30 g 27 , 36 , 45 h 24 , 48 , 1204 Find the largest multiple of:
a 11 which is less than 200 b 17 which is less than 500 :5 Find the smallest multiple of:
a 9 which is more than 300 b 23 which is more than 8000.6 Find the LCM of:
a 3 , 8 b 6 , 8 c 14 , 21 d 9 , 24
e 2 , 3 , 5 f 2 , 4 , 7 g 3 , 5 , 10 h 9 , 12 , 187 Find the highest common multiple of:
a 9 and 12 that is less than 40 b 5 and 15 that is less than 80.8 Three bells chime once at intervals of 3 , 5 and 12 seconds respectively. They first chime at exactly the
same instant. After how many seconds will all three again chime simultaneously?9 Ifaandbare positive integers, the LCM ofaandbcan be found by multiplyingaandband then
dividing the result by their HCF. Check your answers to 6 using this method.EXERCISE C
IGCSE01
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Y:\HAESE\IGCSE01\IG01_AS\008IGCSE01_AS.CDR Wednesday, 10 September 2008 2:10:59 PM PETER
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