How do you make a list of possible pairs of numbers that have a LCM of 48?

Answer 1

#14# such pairs, which are #(1,48),(2,48),(3,48),(4,48),(6,48)#

#(8,48),(12,48),(16,48),(24,48},(48,48),(3,16),(6,16),(12,16),(24,16)#

First of all pairing #48# with all of its factors i.e. #{1,2,3,4,6,8,12,16,24,48}#. This gives us #10# such pairs.
We can also add #(3,16)#, as they are relatively coprime. Further, selecting multiples of #3# will also lead to the pairs #(6,16),(12,16),(24,16)#
Hence in all #14# such pairs, which are
#(1,48),(2,48),(3,48),(4,48),(6,48),(8,48),(12,48),(16,48),(24,48},(48,48),(3,16),(6,16),(12,16),(24,16)#
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Answer 2

To make a list of possible pairs of numbers that have a least common multiple (LCM) of 48, consider the prime factorization of 48, which is (2^4 \times 3). Then, generate pairs of numbers using these prime factors. For example:

  1. Pair 1: (48, 1)
  2. Pair 2: (24, 2)
  3. Pair 3: (16, 3)
  4. Pair 4: (12, 4)
  5. Pair 5: (8, 6)
  6. Pair 6: (6, 8)
  7. Pair 7: (4, 12)
  8. Pair 8: (3, 16)
  9. Pair 9: (2, 24)
  10. Pair 10: (1, 48)

These pairs represent numbers whose LCM equals 48.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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