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Artemon [7]
3 years ago
14

Find the LCM and GCF for 30 and 48.

Mathematics
1 answer:
AlladinOne [14]3 years ago
7 0

LCM is 240

GCF is 6

<em>long explanation</em>

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

LCM(a,b) = ( a × b) / GCF(a,b)

We will now calculate the prime factors of 30 and 48, than find the greatest common factor (greatest common divisor (gcd) of the numbers by matching the biggest common factor of 30 and 48.

Step-1: Prime Factorization of 30

30 = 2^1 × 3^1 × 5^1

Step-2: Prime Factorization of 48

48 = 2^4 × 3^1

Step-3: Factors of 30

1, 2, 3, 5, 6, 10, 15

Step-4: Factors of 48

1, 2, 3, 4, 6, 8, 12, 16, 24

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30 and 48. The biggest common factor number is the GCF number.

So the greatest common factor 30 and 48 is 6.

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Eddi Din [679]
It doesn't matter what's between it as long as it is within that range, if that makes any sense.

1.25 isn't.
1.75 isn't.
1.83 isn't.

1.625 would be your answer. :)
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3 years ago
In circle J with m<br> a. 46.5'<br> b.73'<br> c.292'<br> d.214'
arlik [135]

Answer:

B. 73°

Step-by-step explanation:

<em>m</em><em>L</em><em> </em>HLK = ½ × <em>mL</em><em> </em>HJK = ½×146=73°

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3 years ago
4/3x3.14x5x5x5 volume
Lena [83]
523.6 m3 i hope this helps mark me as brainliest
5 0
3 years ago
The value of a motorbike depreciates by 32% per year. Work out the current value of a motorbike bought 5 years ago for £3600
DaniilM [7]
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3 0
3 years ago
Solve the equation by factoring. 8x^2+10x-7=0<br><br> What is the solution set?
nydimaria [60]

Answer:

\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}

Step-by-step explanation:

Given: 8x² + 10x - 7 = 0

<u>When factoring trinomials of the form ax² + bx + c</u>:

  • multiply the leading coefficient and the last term.
  • find the product factors that add to give you the coefficient of the middle term.
  • rewrite the polynomial with those factors replacing the middle term.

1. Split the middle term:

⇒ 8 × -7 = -56 [multiply the leading coefficient and the last term]

⇒ 14, -4 [find the product factors that add to the middle term's coefficient]

⇒ 8x² + 14x - 4x - 7 = 0 [rewrite with those factors replacing the middle term.]

2. Factor by grouping:

⇒ 8x² + 14x - 4x - 7 = 0 [factor out 2x]

⇒ 2x(4x + 7) - 4x - 7 = 0 [factor out -1 or the negative sign]

⇒ 2x(4x + 7) -1(4x + 7) = 0 [factor out 4x + 7]

⟹ (4x + 7)(2x - 1) = 0

3. Separate into 2 cases:

  1. 4x + 7 = 0
  2. 2x - 1 = 0

 

<u><em>Case 1:</em></u>

⇒ 4x + 7 = 0 [subtract 7 from both sides]

⇒ 4x + 7 - 7 = 0 - 7

⇒ 4x = -7 [divide both sides by 4]

⇒ 4x ÷ 4 = -7 ÷ 4

⟹ x = \bold{-\dfrac{7}{4}}

<u><em>Case 2:</em></u>

⇒ 2x - 1 = 0 [subtract 1 from both sides]

⇒ 2x - 1 + 1 = 0 + 1

⇒ 2x = 1 [divide both sides by 2]

⇒ 2x ÷ 2 = 1 ÷ 2

⟹ x = \bold{\dfrac{1}{2}}

Solutions:

\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}

Learn more about quadratic equations here:

brainly.com/question/27750885

brainly.com/question/27739892

brainly.com/question/27638369

7 0
2 years ago
Read 2 more answers
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