jill is thinking of two numbers. they have the sum of 27 and a difference of 7. what are the two numbers?
2 answers:
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The LCM of 18 and 24 using the prime-factorization method is <u>72</u>.
The LCM of 27, 81, and 54, using the division method is <u>162</u>.
In the first question, we are asked to find the LCM of the given numbers using the prime factorization method.
(i) 18, 24.
Prime factorization gives:
18 = 2*3², and 24 = 2³*3.
The LCM is the product of the highest power of each prime factor.
Thus, LCM = 2³*3² = 8*9 = 72.
Thus, the LCM of 18 and 24 using the prime-factorization method is <u>72</u>.
Doing similarly for other sub-parts, The LCM of:
(ii) 16, 40 is 80.
(iii) 30, 36 is 180.
(iv) 28, 44 is 308.
(v) 20, 32 is 160.
(vi) 20, 135 is 540.
(vii) 45, 75 is 225.
(viii) 36, 84 is 252.
(ix) 12, 18, 24 is 72.
(x) 25, 35, 45 is 1575.
(xi) 9, 15, 21 is 315.
(xii) 25, 50, 75 is 150.
In the second question, we are asked to find the LCM of the given numbers, using the division method.
(i) 27, 81, 54.
The division method gives:
The LCM is the product of all the numbers used for division.
LCM = 2*3*3*3*3*1 = 162.
Thus, the LCM of 27, 81, and 54, using the division method is <u>162</u>.
Doing similarly for other sub-parts, The LCM of:
(ii) 18, 45, 63 is 630.
(iii) 35, 55, 100 is 7700.
(iv) 210, 140, 315 is 1260.
(v) 112, 120, 150 is 8400.
(vi) 144, 180, 300 is 3600.
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The answer is C.
To solve these types of equations you first need to make sure that you equation is equal to 0. In this case all of the numbers are already on the same side so no work needs to be done there. Then we can get a, b and c values for the quadratic equation by looking at the coefficients.
a = 4 (number attached to x^2)
b = -6 (number attached to x)
c = 1 (number with no variable attached)
Now we can put this into the quadratic equation.
To solve these types of equations you first need to make sure that you equation is equal to 0. In this case all of the numbers are already on the same side so no work needs to be done there. Then we can get a, b and c values for the quadratic equation by looking at the coefficients.
a = 4 (number attached to x^2)
b = -6 (number attached to x)
c = 1 (number with no variable attached)
Now we can put this into the quadratic equation.