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## Find the least common multiple of x2 + x – 12 and x2 + 2x -15?

To factor x^2 + x – 12 into (x + a)(x + b), FOIL tells us that a + b = the coefficient of the middle term x which is 1, and (a)(b) = the last term which is -12

So we have

a + b = 1 (which we can rearrange into b = 1 – a) and

ab = -12

Substituting (1 – a) for b, we get

ab = -12

a(1 – a) = -12

a – a^2 = -12

0 = a^2 – a – 12

Using the quadratic formula, we get

a = (-(-1) +- √((-1^2) – (4)(1)(-12))) / (2 * 1)

a = (1 +- √(1 + 48)) / 2

a = (1 +- √(49)) / 2

a = (1 +- 7) / 2

which gives us two possible answers

a = (1 + 7) / 2

a = 4

and

a = (1 – 7) / (2)

a = -3

Therefore, (x + 4) and (x – 3) are two factors for the polynomial x^2 + x – 12

To factor x^2 + 2x – 15 into (x + a)(x + b), FOIL tells us that a + b = the coefficient of the middle term 2x which is 2, and (a)(b) = the last term which is -15

So we have

a + b = 2 (which we can rearrange into b = 2 – a) and

ab = -15

Substituting (2 – a) for b, we get

ab = -15

a(2 – a) = -15

2a – a^2 = -15

0 = a^2 – 2a – 15

Using the quadratic formula, we get

a = (-(-2) +- √((-2^2) – (4)(1)(-15))) / (2 * 1)

a = (2 +- √(4 + 60)) / 2

a = (2 +- √(64)) / 2

a = (2 +- 8) / 2

which gives us two possible answers

a = (2 + 8) / 2

a = 5

and

a = (2 – 8) / (2)

a = -3

Therefore, (x + 5) and (x – 3) are two factors for the polynomial x^2 + x – 12

Now that we have factored both equations, what are the common factors for both equations?

(x – 3) is common to both

So we include it in the LCM

Next, what are the un-common factors for both equations?

(x + 4) appears in the first but not in the second

(x + 5) appears in the second but not in the first

So we include both in the LCM as multipliers

Therefore, the LCM for this problem is:

(x – 3)(x + 4)(x + 5)

Find the least common multiple of x2 + x – 12 and x2 + 2x -15? – To factor x^2 + 2x – 15 into (x + a)(x + b), FOIL tells us that a + b = the coefficient of the middle term 2x which is 2, and (a)(b) = the last term which is -15. (x + 5) appears in the second but not in the first. So we include both in the LCM as multipliers. Therefore, the LCM for this problem isLCM of 9 and 12, find the lowest common denominator (lcd) smallest multiple of two integers, learn what is the least common LCM Calculator. What is the Least Common Multiple of 9 and 12? Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 12.Consider the form. . Find a pair of integers whose product is. . Write the factored form using these integers. The LCM is the smallest positive number that all of the numbers divide into evenly. 1. List the prime factors of each number.

Least Common Multiple of 9 and 12 LCM(9,12) – Prealgebra Factors and Multiples Least Common Multiple. The multiples of 12 are 12,24,36, 48, 60 The smallest number which is a multiple of both 10 and 12 is 60. Or express both numbers in prime factor form: 10 =2×5 12=2x2x3 2 is common to both so the LCM is 2x2x3x5=60.Find the least common multiple of $4x^2 – 16$ and $6x^2 – 24x + 24$. Solution. Step 1 Factor each polynomial. Write numerical factors as products of So you put the regular numbers as products of primes (the $2^2$), and then… you have the $2^2$ and the normal 2, so you just put the highest…Using a factor tree to find the least common multiple (LCM) of two numbers. This video is provided by the Learning Assistance Center of Howard Community…

Find the LCM x^2+x-12 , x^2+2x-15 | Mathway – In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined…See how to find the Least Common Multiple of any number using our Least Common Multiplier (LCM) Calculator. Use this calculator to find the Least Common Multiple (LCM) for up to 3 mumbers. Note that 6 = 6 x 1, 12 = 6 x 2, 18 = 6 x 3, 24 = 6 x 4, 30 = 6 x 5.Well, the LCM of 6 and 9 is 18. List multiples of the bigger one, so multiples of 9: 9,18,27,36,45…. Then find the first one in the list that divides by the other number(s), in this case, 6.