What is the LCD of #\frac { 9} { 14}# and #\frac { 5} { 21}#?

Answer 1

Nathan Axel

42

14 can be factored into 2 x7 21 can be factored into 3 x 7

The seven is a common factor and only needs to be used once. so

LCD = # 2 xx 3 xx 7 = 42#

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Answer 2

Eva Abramson

The least common denominator (LCD) of fractions is the least common multiple (LCM) of their denominators.

The denominators of the fractions $\frac{9}{14}$ and $\frac{5}{21}$ are 14 and 21 respectively.

The LCM of 14 and 21 can be found by determining the least common multiple of their prime factors:

Prime factorization of 14: $2 \times 7$
Prime factorization of 21: $3 \times 7$

The LCM must include all the prime factors with the highest power:

$\text{LCM}(14, 21) = 2 \times 3 \times 7 = 42$

Therefore, the LCD of $\frac{9}{14}$ and $\frac{5}{21}$ is 42.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.