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Finding the Lowest Common Denominator>
Finding the Lowest Common DenominatorFinding the Lowest Common Denominator
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Question 1 of 6
1. Question
Find the lowest common denominator (LCD) of`6x` and `16x^2`Hint
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The lowest common denominator (LCD) can also be referred to as the least common multiple (LCM).First, decompose each term into its smallest factors.`6x` `:` `2`,`3`, `x` `16x^2` `:` `2`,`2,2,2,``x`,`x` Combine the red terms and multiply to the black ones.`\text(LCD)` `:` `2`,`x`,`3,2,2,2,x` `:` `2``xx``x``xx 3 xx 2 xx 2 xx 2 xx x` Multiply the factors `:` `48x^2` `48x^2` -
Question 2 of 6
2. Question
Find the lowest common denominator (LCD) of`x-3` and `3x+5`Correct
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The lowest common denominator (LCD) can also be referred to as the least common multiple (LCM).First, look for the factors of the given terms.`x-3` `:` `x-3, 1` `3x-5` `:` `3x-5, 1` Since `1` is the only common factor, then we can find the LCD.`\text(LCD)` `:` `(x-3)(3x+5)` `(x-3)(3x+5)` -
Question 3 of 6
3. Question
Find the lowest common denominator (LCD) of`(x-2)^2` and `x^2+2x+8`Hint
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The lowest common denominator (LCD) can also be referred to as the least common multiple (LCM).First, decompose each term into its smallest factors.`(x-2)^2` `=` `(x-2) xx (x-2)` Since the second term is in standard form `(``a``x^2+``b``x+``c``=0)` we can factorise using the cross method.`x^2+``2``x``-8``=0`To factorise, we need to find two numbers that add to `2` and multiply to `-8``4` and `-2` fit both conditions`4 – 2` `=` `2` `4 xx -2` `=` `-8` 
Read across to get the factors.`(x+4)(x-2)=0`Write the factors of the two polynomials next to each other.`(x-2)^2` `=` `(x-2)``(x-2)` `x^2+2x-8` `=` `(x+4)``(x-2)` Combine the red terms and multiply to the black ones.`\text(LCD)` `=` `(x-2)``(x-2)(x+4)` `(x-2)(x-2)(x+4)` -
Question 4 of 6
4. Question
Find the lowest common denominator (LCD) of`x^2-5x+6` and `x^2-x-6`Hint
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The lowest common denominator (LCD) can also be referred to as the least common multiple (LCM).Since the first polynomial is in standard form `(``a``x^2+``b``x+``c``=0)` we can factorise using the cross method.`x^2``-5``x+``6``=0`To factorise, we need to find two numbers that add to `-5` and multiply to `6``-3` and `-2` fit both conditions`-3 – 2` `=` `-5` `-3 xx -2` `=` `6` 
Read across to get the factors.`(x-3)(x-2)=0`Since the first polynomial is in standard form `(``a``x^2+``b``x+``c``=0)` we can factorise using the cross method.`x^2``-``x``-6``=0`To factorise, we need to find two numbers that add to `-1` and multiply to `-6``-3` and `2` fit both conditions`-3 + 2` `=` `-1` `-3 xx 2` `=` `-6` 
Read across to get the factors.`(x-3)(x+2)=0`Write the factors of the two polynomials next to each other.`x^2-5x+6` `=` `(x-3)``(x-2)` `x^2-x-6` `=` `(x-3)``(x+2)` Combine the red terms and multiply to the black ones.`\text(LCD)` `=` `(x-3)``(x-2)(x+2)` `(x-3)(x-2)(x+2)` -
Question 5 of 6
5. Question
Find the lowest common denominator (LCD) of`x+4` and `x^2+8x+16`Hint
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The lowest common denominator (LCD) can also be referred to as the least common multiple (LCM).Since the second polynomial is in standard form `(``a``x^2+``b``x+``c``=0)` we can factorise using the cross method.`x^2+``8``x+``16``=0`To factorise, we need to find two numbers that add to `8` and multiply to `16``4` and `4` fit both conditions`4 + 4` `=` `8` `4 xx 4` `=` `16` 
Read across to get the factors.`(x+4)(x+4)=0`Write the factors of the two polynomials next to each other and mark similar factors.`x+4` `=` `(x+4)``(1)` `x^2+8x+16` `=` `(x+4)``(x+4)` Combine the red terms and multiply to the black ones.`\text(LCD)` `=` `(x+4)``(x+4)` `(x+4)(x+4)` -
Question 6 of 6
6. Question
Find the lowest common denominator (LCD) of`x`, `x+2` and `x^2-4`Hint
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The lowest common denominator (LCD) can also be referred to as the least common multiple (LCM).First, decompose each term into its smallest factors.`x` `=` `x xx 1` `x+2` `=` `(x+2) xx 1` `x^2-4` `=` `(x-2)(x+2)` Write the factors of the two polynomials next to each other and mark similar factors.`x` `:` `x,1` `x+2` `:` `(x-2)`,`1` `x^2-4` `:` `(x-2)`,`(x+2)` Combine the red terms and multiply to the black ones.`\text(LCD)` `=` `(x-2)``x(x+2)` `=` `x(x+2)(x-2)` `x(x+2)(x-2)`