Question

Find the least square number which is exactly divisible by 21 , 36 and 48. Also state the sq.

root of the number got without actual calculation.​

Answer 1

Hey mate,

Prime factorization of the numbers:

21 = 3 × 7

36 = 2 × 2 × 3 × 3

48 = 2 × 2 × 2 × 2 × 3

LCM(21, 36, 48)

= 2 × 2 × 2 × 2 × 3 × 3 × 7

= 1008

now to make it perfect square, we have multiple with 7 to get it exactly it divisible by 21 , 36 and 48.

=1008 × 7

=7056

Now $\sqrt{7056\\}$ is

  =$\sqrt{2*2*2*2*3*3*7*7}$

  =$\sqrt{16*9*49}$

   = 4*3 *7*$\sqrt{1}$

   =84

84 is the square root of the number without calculation.

∴ The least divisible number is 7056

and its sq. root is 84.

Answer 2

Answer:

Hey mate,

Prime factorization of the numbers:

21 = 3 × 7

36 = 2 × 2 × 3 × 3

48 = 2 × 2 × 2 × 2 × 3

LCM(21, 36, 48)

= 2 × 2 × 2 × 2 × 3 × 3 × 7

= 1008

now to make it perfect square, we have multiple with 7 to get it exactly it divisible by 21 , 36 and 48.

=1008 × 7

=7056

Now \begin{gathered}\sqrt{7056\\}\end{gathered} is

=\sqrt{2*2*2*2*3*3*7*7}

2∗2∗2∗2∗3∗3∗7∗7

=\sqrt{16*9*49}

16∗9∗49

= 4*3 *7*\sqrt{1}

1

=84

84 is the square root of the number without calculation.

∴ The least divisible number is 7056

and its sq. root is 84.