Aqua 3. Find the smallest perfect square that is exactly divisible by each of the following numbers (a) 8, 9 and 10 (b)

Question

Aqua
3.
Find the smallest perfect square that is exactly divisible by each of the following numbers
(a) 8, 9 and 10
(b) 8. 15 and 20
(c) 6. 9 and 15
4. Check by prime factorisation method, which of the followi
are perfect squares?​

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Margaret 2 weeks 2021-09-10T12:34:42+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-09-10T12:36:07+00:00

    Answer:

    (a) 3600

    (b) 3600

    (c) 900

    Step-by-step explanation:

    We know that,

    The smallest perfect square must be divisible by all the numbers given,

    So, for that to happen, it must be a multiple of the given numbers (Think about it…..)

    Only if a number is a multiple of another number can it be divisible,

    For ex:- 8 is a multiple of 4

    Thus, 8 is divisible by 4, 8 ÷ 4 = 2

    Now, back to our Question,

    (a)

    Thus, to find a number which is divisible by 8, 9 and 10

    We must find its LCM of 8, 9 and 10

    LCM = 360

    Now, if we take the square root of 360 we will not get a perfect square because its prime factorization in not in pairs,

    360 = 2 × 2 × 2 × 3 × 3 × 5

    Here 2 and 5 is not in a pair so we must multiply 2 and 5 with 360,

    360 × 2 × 5

    = 360 × 10

    = 3600

    Now, it is a Perfect square because,

    3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5

    Since all numbers are in pair and it is divisible by 8, 9 and 10.

    Thus, the smallest perfect square that is exactly divisible by 8, 9 and 10 is 3600

    (b)

    Similarly,

    LCM of 8, 15 and 20 = 120

    Now,

    120 = 2 × 2 × 2 × 3 × 5

    Here 2, 3 and 5 is not in pairs so 120 is not a perfect square,

    thus, we must make it by multiply 2, 3 and 5 to 120.

    = 120 × 2 × 5 × 3

    = 120 × 10 × 3

    = 360 × 10

    = 3600

    Thus, the smallest perfect square that is exactly divisible by 8, 15 and 20 is 3600.

    (c)

    Here also same process,

    LCM of 6, 9 and 15 = 90

    Now,

    90 = 2 × 3 × 3 × 5

    Again 90 is not a perfect square because its 2 and 5 are not in pairs so we multiply 2 and 5 to 90

    = 90 × 2 × 5

    = 90 × 10

    = 900

    Thus, the smallest perfect square that is exactly divisible by 6, 9 and 15 is 900

    Hope it helped and you understood it……..All the best

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