All categories

3 years ago

What is the smallest 4-digit positive number divisible by 2, 3, 4, 5, 6, 8, 9, and 10?

Mathematics

1 answer:

Kruka [31]3 years ago

3 0

<h3>Answer: 1080</h3>

===================================================

Explanation:

let's find the prime factorization for each value. If the value is prime, then just move onto the next value

2 = 2 ... already prime, nothing needed to do here

3 = 3

4 = 2*2

5 = 5

6 = 2*3

8 = 2*2*2

9 = 3*3

10 = 2*5

The list of prime factors that show up are: {2, 3, 5}

We have '2' show up at most 3 times, the prime '3' show up at most 2 times, and the prime '5' show up at most 1 time.

This means 2^3*3^2*5 = 360 is the LCM of the list {2,3,4,5,6,8,9,10}

Any multiple of 360 will also be a common multiple of the original list of values.

Multiples of 360: {360, 720, 1080, ...}

We see that 1080 is the smallest 4-digit multiple of 360.

You might be interested in

Austin and Aaron were running for mayor in a small town. Aaron received 54% of the votes. Austin received 3266 votes. How many v

lora16 [44]

Answer: dog

Step-by-step explanation:

so basically 70 plus 7 equals 9 and then u ride the car with the horse while eating a fish. how much burgers did he eat?

7 0

4 years ago

Solve the proportion

mario62 [17]

Answer:

$\boxed{\sf x = 5}$

Step-by-step explanation:

$\sf Solve \: for \: x \: over \: the \: real \: numbers: \\ \sf \implies \frac{2}{x - 3} = \frac{5}{x} \\ \\ \sf Take \: the \: reciprocal \: of \: both \: sides: \\ \sf \implies \frac{x - 3}{2} = \frac{x}{5} \\ \\ \sf Expand \: out \: terms \: of \: the \: left \: hand \: side: \\ \\ \sf \implies \frac{x}{2} - \frac{3}{2} = \frac{x}{5} \\ \\ \sf Subtract \: \frac{x}{5} - \frac{3}{2} \: from \: both \: sides: \\ \sf \implies \frac{x}{2} - \frac{3}{2} - ( \frac{x}{5} - \frac{3}{2} ) = \frac{x}{5} - ( \frac{x}{5} - \frac{3}{2} ) \\ \\ \sf \implies \frac{x}{2} - \frac{3}{2} - \frac{x}{5} + \frac{3}{2} = \frac{x}{5} - \frac{x}{5} + \frac{3}{2} \\ \\ \sf \frac{x}{5} - \frac{x}{5} = 0 : \\ \sf \implies \frac{x}{2} - \frac{x}{5} - \frac{3}{2} + \frac{3}{2} = \frac{3}{2} \\ \\ \sf \frac{3}{2} - \frac{3}{2} = 0: \\ \sf \implies \frac{x}{2} - \frac{x}{5} = \frac{3}{2} \\ \\ \sf \frac{x}{2} - \frac{x}{5} = \frac{5x - 2x}{10} = \frac{3x}{10} : \\ \sf \implies \frac{3x}{10} = \frac{3}{2} \\ \\ \sf Multiply \: both \: sides \: by \: \frac{10}{3} : \\ \sf \implies \frac{3x}{10} \times \frac{10}{3} = \frac{3}{2 } \times \frac{10}{3} \\ \\ \sf \frac{3x}{10} \times \frac{10}{3} = \cancel{\frac{3}{10} } \times( x) \times \cancel{ \frac{10}{3} } = x : \\ \sf \implies x = \frac{3}{2} \times \frac{10}{3} \\ \\ \sf \frac{3}{2} \times \frac{10}{3} = \cancel{ \frac{3}{2} } \times \cancel{ \frac{3}{2} } \times 5 : \\ \sf \implies x = 5$

8 0

3 years ago

10. What is the solution to 5x2 - 7x + 3 = 0?

masya89 [10]

Answer:

Bodmas rules first -7 multiplay by 3 and get -21 the 5 multiply by 2 and get 10 ..then +10 minus 21 and get -11

3 0

4 years ago

Helpppppppppppppppppppppppppppppppppppp

Vadim26 [7]

Answer:

m = - 1

Step-by-step explanation:

9m + 13 = 4

subtract 13 from both sides

9m = 4 - 13

9m = - 9

divide both sides by 9

m = - 1 (negative 1)

5 0

3 years ago

A garden is designed in the shape of a rhombus formed

Usimov [2.4K]

Answer:

120ft.

Step-by-step explanation:

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet. What is the distance around the perimeter of the garden? 120ft.

4 0

3 years ago