Mathematics, 10.07.2019 15:10 tatiiiee

The smallest number which is divisible by both 306 and 657

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22,338 is the smallest number that is divisible by both 306 and 657. In other words, 22,338 is the least common multiple of 306 and 657.

Step-by-step explanation:

The question is asking for the smallest number that is divisible by 306 and 657. That number in question is also known as the least common multiple of 306 and 657.

Neither 306 nor 657 is prime; the two numbers themselves are made of prime factors. For the number in question to be divisible by both 306 and 657, it needs to include the factors of both 306 and 657. However, for this number to be as small as possible, it needs to contain only the necessary factors and nothing else.

To find the factors required for this number, start by finding all the prime factors of the two divisors.

$\begin{aligned}306&=2 \times 153\\ &= 2\times 3 \times 51\\ &= 2 \times 3 \times 3 \times 17 \\ &= 2 \times 3^{2} \times 17\end{aligned}$ .

In other words, the prime factors of 306 are:

One

, Two

s, andOne

Similarly,

$\begin{aligned}657&= 3 \times 219\\ & = 3 \times 3 \times 73\\&=3^{2}\times 73 \end{aligned}$ .

The prime factors of 657 are:

Two

s, andOne

$\begin{array}{l||l|l||l}\text{Factor}& 306 & 657 & \text{New Number}\\\cline{1-4} \\[-1.0em]2 &\text{1 Occurrence}& \text{0 Occurrence} & \text{1 Occurrence}\\3 &\text{2 Occurrence} & \text{2 Occurrence}& \text{2 Occurrence}\\ 17 &\text{1 Occurrence}& \text{0 Occurrence} & \text{1 Occurrence}\\73 &\text{0 Occurrence}& \text{1 Occurrence} & \text{1 Occurrence}\end{array}$ .

The number in question shall contain at least

One

, Two

,One

, andOne

As a result, that number shall be equal to $2 \times 3^{2}\times 17 \times 73 = 22338$ .

Answer from: Quest

the clues that signal the reader should change tone are the punctuation marks, the grammatical signs. for example, the quotation marks at the beginning of something someone else said literally or the exclamation marks.

the tone of the first line of dialogue until "gettysburg" is a kind tone, a tone of advise. the narrator is trying to the other person in doing something he or she obviously is finding hard to do by giving a piece of advise and bringing up a memory of a successful similar case.

the clue that the reader understand how to read the word "bang" is the exclamation mark. it gives the word a surprise tone, a strong accent.

the best tone for reading the word "bang" is an exciting tone, a surprise one, even a loud one.

the words that should be read with a formal tone are the ones that give factual information. the sentence: mister lincoln couldn't think of anything to say at the gettysburg" gives information about an event and it needs to be read formally, also, when the narrator wants to transmit calmness, a formal and slow tone is needed, because people also transmit messages with the vibrations of our voices and tones.

Answer from: Quest

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step-by-step explanation: vsfdvsfvd

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