Afreen says, “I am thinking of 3 consecutive numbers. The first is a multiple of 4, the second is a multiple of 5 and the third is a multipl

Question

Afreen says, “I am thinking of 3 consecutive numbers. The first is a multiple of 4, the second is a multiple of 5 and the third is a multiple of 6.” What could the numbers be? Can you find 3 possible sets of numbers?

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Ben Gia 6 months 2021-07-20T21:52:00+00:00 1 Answers 33 views 0

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    2021-07-20T21:53:55+00:00

    Answer:

    The 3 ses that we found are:

    {4, 5, 6}

    {64, 65, 66}

    {124, 125, 126}

    Step-by-step explanation:

    3 consecutive numbers are written as:

    n, (n + 1), (n + 2)

    We know that the first one is a multiple of 4.

    Then n is a multiple of 4:

    n = k*4

    where k is an integer.

    The second one is a multiple of 5, then:

    (n + 1) = j*5

    where j is an integer.

    The last one is a multiple of 6.

    (n + 2) = p*6

    where p is an integer.

    We want to find 3 sets.

    The first one is trivial:

    n = 4

    n + 1 = 5

    n + 2 = 6

    4 is a multiple of 4

    5 is a multiple of 5

    6 is a multiple of 6.

    Now let’s find a set that is not trivial.

    First, remember that all the multiples of 5 end with a 0 or a 5,

    Then we can look for a value n, that is multiple of 4, and that has a last units digit equal to 4 (then the next one will have a units digit and will be multiple of 5)

    For example, 4*6 = 24

    24 is a multiple of 4.

    The next number is 24 + 1 = 25, which is multiple of 5.

    The next number is 25 + 1 = 26, which is not multiple of 6.

    So let’s try again.

    4*11 = 44, is a multiple of 4.

    The next number is 44 + 1 = 45

    45 is a multiple of 5.

    The next number is 45 + 1 = 46, which is not multiple of 6

    So we need to try with another set.

    4*16 = 64, is a multiple of 4.

    The next number is 64 + 1 = 65, which is multiple of 5.

    The next number is 66, which is multiple of 6:

    6*11 = 66

    Then the set:

    n = 64

    n + 1 = 65

    n + 2 = 66

    Is a possible set.

    Now we can keep trying this, we can see that the next set  has the numbers:

    n = 4*31  = 124 is a multiple of 4.

    The next number, is 124 + 1 = 125, which is a multiple of 5.

    The next number is 125 + 1 = 126, which is multiple of 6

    6*21 = 126

    Then the set:

    n = 124

    n + 1 = 125

    n + 2 = 126

    Is another possible set.

    The 3 ses that we found are:

    {4, 5, 6}

    {64, 65, 66}

    {124, 125, 126}

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