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?
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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?
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