
Concept explainers
Luke's LCMs
Luke has a set of cards numbered 1 to 8, which he arranges in pairs. He notes the sum of the numbers on each pair of cards and calculates the lowest common multiple (LCM) of the four sums. For example the pairs could have been (7,3) (2,6) (5,1) (8,4).
In this case, the pair sums would have been 10,8,6,12 respectively, giving an LCM of 120. Pair sums are not necessarily different.
A) Explain why Luke could not obtain an LCM of 39.
B) Luke now takes 20 cards numbered from 1 to 20. Show how the cards can be paired to give an LCM of 60.
C) Luke now takes six cards numbered 1 to 6 but he groups them into two sets of three. He finds the sums of the numbers in each triple and then finds the LCM of these two triple sums. What is the smallest LCM he could obtain?

Trending nowThis is a popular solution!
Step by stepSolved in 2 steps

- For a segment of a radio show, a disc jockey can play 9 records. If there are 14 records to select from, in how many ways can the program for this segment be arranged? waysarrow_forwardChandler is a magician performing at a birthday party. Chandler first performs one of 3 card tricks, which is followed by one of 2 coin tricks. How many different magic shows can Chandler perform?arrow_forwardTell wether each problem represets a permutation or a combination. Then solve the problem. Brandon has 8 different plates with which to set the table. How many different ways can he place the plates? In how many ways can Mia choose 10 mugs fro a collection of 15? How many ways can 7 clarinet players be seated in 7 chairs in the concert band?arrow_forward
- An artist is selling children's crafts. Necklaces cost $2.25 each, and bracelets cost $1.50 per each.Select ALL the combinations of necklaces and bracelets that the artist could sell for exactly $12.00. * 5 necklaces and 1 bracelet 2 necklaces and 5 bracelets 3 necklaces and 3 bracelet 4 necklaces and 2 bracelets 3 necklaces and 5 bracelets 6 necklaces and no bracelets No necklaces and 8 bracelets This is a required questionarrow_forwardToward the end of a game of Scrabble you hold the letters D,O,G and Q. You can choose three of these four letters and arrange them in order in how many different ways?arrow_forward
- Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,





