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Least Common Multiple Of 13

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									                                            Emirates College for Advanced Education
                                            Foundation Year
                                            Mathematics 2



Lesson 6               Least Common Multiple (LCM )                    Name:
Spring 2008                                                            Worksheet
         Definition of LCM
        The least common multiple (LCM) is the smallest common multiple
        of two or more numbers.

        We shall write the least common multiple of a and b as LCM (a, b)


 1. Find the LCM (a, b) by listing multiples of a and b.

   (a) LCM (12, 15)                                        (e) LCM (42, 24)




   (b) LCM (7, 13)                                         (f) LCM (13, 26, 39)




    (c) LCM (17, 51)                                       (g) LCM (30, 40, 60)




   (d) LCM (24, 36)
M2/Q1s3                            – Page 2 of 4 –                           Name:


         Method of using prime factorization:
        After the numbers are expressed in prime factorization form, take the
        product of all the prime factors raised to the highest possible power.


2. Find the LCM of the following numbers.

   (a) 12, 15




   (b) x = 25 · 36 · 7 and y = 32 · 72 · 11




   (c) x = 25 · 32 · 57 ,   y = 24 · 34 · 53 · 7 and z = 2 · 36 · 54 · 132
M2/Q1s3                        – Page 3 of 4 –                     Name:

3. Use prime factorization to find LCM (48, 50)




4. Use prime factorization to find the following:

   (a) LCM (288, 39)




           288 × 39
   (b)
         LCM (288, 39)




          Theorem 1:
         For any two natural numbers a and b, the relationship
         between the GCD and LCM are connected by the equation

         GCD(a, b) × LCM (a, b) = a × b


5. Use theorem 1 to find the LCM of the following.

   (a) 48, 60                                       (b) 126, 384
M2/Q1s3                         – Page 4 of 4 –                        Name:


          Applications of LCM (a, b) in adding and subtraction fractions.


         • Find the multiples of each denominator.
         • Use the lowest common multiple as the new denominator.
           (This called the least common denominator (LCD))
         • Rewrite the fractions using the least common denominator.



6. Find the following.

         1 1                                                  5 1
   (a)    +                                             (c)    −
         3 5                                                  6 8




         3 2                                                  4 2
   (b)    +                                             (d)    −
         7 8                                                  5 3




          Word Problems involving LCM (a, b).

7. Fatima is buying hot dogs for a class picnic. Hot dogs are are sold in packages of 10.Hot dogs burns are
   are sold in packages of 8. What is the smallest number of hot dogs and burns Fatima can buy to have
   an equal number of each?




8. Two bus services A and B arrive at a station. Service A arrives at the station every 15 minutes;
   service B arrives at the station every 20 minutes. The first bus arrives at the station at 8 : 00am.
   When will both buses arrive at the station again?

								
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