asked 90.9k views
2 votes
The lowest common denominator (LCD) for a set of fractions is the smallest number that the

denominators of those fractions will divide into evenly.
A. Yes
B. No
C. Maybe
D. Sometimes
E. Not Applicable

1 Answer

2 votes

Explanation:

"evenly" ? no.

"evenly" would mean to equal parts. that is not the case for different denominators. only for equal ones, and then there is no transformation necessary.

let's say, we want to add

1/14 and 1/32

the LCD (or LCM - the lowest common multiple) is found by looking at the prime factors and by creating the combination of the longest chains of each prime factor.

14 / 2 = 7

7 / 2 no

7 / 3 no

7 / 5 no

7 / 7 = 1

finished.

so, the prime factors of 14 are 2, 7.

32/2 = 16

16/2 = 8

8/2 = 4

4/2 = 2

2/2 = 1

finished.

the prime factors of 32 are 2, 2, 2, 2, 2.

the LCD or LCM is the combination of the longest chains

2×2×2×2×2 × 7 = 32×7 = 224

224 / 14 = 16

224 / 32 = 7

the LCD or LCM is the smallest number that each denominator will divide into without any reminder.

that should be the correct definition.

if you understand "evenly" with the same meaning, then by all means say yes.

as explained, I understand it differently, and therefore I say no.

answered
User Louis Strous
by
8.2k points
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