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3 years ago

find the least perfect square that is exactly divisible by each of the numbers 5 , 18 , 25 and 27 .

Mathematics

1 answer:

Dimas [21]3 years ago

7 0

<h3>☂︎ Answer :- </h3>

8100

<h3>☂︎ Solution :- </h3>

LCM of 5 , 18 , 25 and 27 = 2 × 3³ × 5²
2 and 3 have odd powers . To get a perfect square, we need to make the powers of 2 and 3 even . The powers of 5 is already even .

In other words , the LCM of 5 , 18 , 25 and 27 can be made a perfect square if it is multiplied by 2 × 3 .

The least perfect square greater that the LCM ,

☞︎︎︎ 2 × 3³ × 5² × 2 × 3

☞︎︎︎ 2² × 3⁴ × 5²

☞︎︎︎ 4 × 81 × 85

☞︎︎︎ 100 × 81

☞︎︎︎ 8100

8100 is the least perfect square which is exactly divisible by each of the numbers 5 , 18 , 25 , 27 .

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Gelneren [198K]

<h3>18 months will pass before the two friends have the same hair length</h3>

<em><u>Solution:</u></em>

Let "x" be the number of months

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$Equation : 13 + \frac{2}{3}x ------- eqn\ 1$

Her friend Kate’s hair is 16 inches long and grows at an average rate of ½ in per month

$Equation: 16 + \frac{1}{2}x ----- eqn\ 2$

<em><u>For two friends to have the same hair length, eqn 1 must be equal to eqn 2</u></em>

$13 + \frac{2x}{3} = 16 + \frac{x}{2}\\\\\frac{2x}{3} - \frac{x}{2} = 16 - 13\\\\\frac{4x}{6} - \frac{3x}{6} = 3\\\\x = 18$

Thus 18 months will pass before the two friends have the same hair length

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find the least perfect square that is exactly divisible by each of the numbers 5 , 18 , 25 and 27 . ​

find the least perfect square that is exactly divisible by each of the numbers 5 , 18 , 25 and 27 .