Lowest Common Multiple

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					Learning Enhancement

Steps into Numeracy

Lowest Common Multiple
This guide introduces the idea of a lowest common multiple for a given
list of numbers and also offers techniques for finding it.

What is a lowest common multiple?

The lowest common multiple (LCM) is the smallest number that is a common multiple of
two or more numbers. Finding these numbers is particularly useful when adding and
subtracting fractions as the most efficient common denominator to pick is the lowest
common multiple of the denominators. It is essential that you can factorise a number
into its prime factors (see study guide: Prime Factors).

For small numbers, finding their LCM is relatively straightforward. List the times tables
for each number and identify the smallest number which is common to each list.

Example:         What is the LCM of 8 and 12

       Multiples of 8:          8, 16, 24, …
       Multiples of 12:         12, 24, …

Thus the LCM of 8 and 12 is 24.

For larger numbers, there is a more robust technique to follow. (Note that this method
also works for smaller numbers.)

    Step 1:      Write the numbers in prime factor form.
    Step 2:      Find the prime factors that are common to both lists.
    Step 3:      Delete the factors common in both lists from that of the smaller number.
    Step 4:      Multiply the larger number by the remaining prime factors of the smaller
                 number. This gives the LCM.

Example:         What is the LCM of 240 and 924?

       Step 1:          In terms of prime factors, 240 = 2 × 2 × 2 × 2 × 3 × 5

                            In terms of prime factors, 924 = 2 × 2 × 3 × 7 × 11

          Step 2:           You have 2 × 2 × 3 common in both lists.

          Step 3:           After deleting these from the prime factors of 240 you have
                            2 × 2 × 5 left over.

          Step 4:           You multiply 2 × 2 × 5 by 924 to give:
                            LCM (240, 924) = (2 × 2 × 3 × 7 × 11) × (2 × 2 × 5 ) = 924 × 20 = 18480

Try these. Find the LCM of the following numbers (the answers are at the bottom of this

(i)       24 and 62 (744)           (ii)     13 and 43 (559)        (iii)   234 and 612 (7956)

Further help and advice
A Learning Enhancement Tutor in the Dean of Students’ office can help you with your
basic mathematical skills. See for more details.

Further guidance and information

If you are still anxious about mathematics, you can talk to your lecturer or Personal
Adviser, or make an appointment to see a Learning Enhancement Tutor in the Dean
of Students’ Office.

Telephone:             01603 593676

There are further resources on many other aspects of numeracy, mathematics, statistics
and science available from the Dean of Students’ Office and on its website:

This guidance leaflet is one of a series on mathematics produced
 by the Dean of Students’ Office at the University of East Anglia.

      Answers: (i) 744 (ii) 559 (iii) 7956                                                            2

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