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21 votes
21 votes
How to find the LCM this way?

if the given denominators are:
(20)(20), (20)(20), (20)(20)

please explain

How to find the LCM this way? if the given denominators are: (20)(20), (20)(20), (20)(20) please-example-1
User Ken Lyon
by
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1 Answer

13 votes
13 votes

Answer:

400

Explanation:

finding the LCM is through analysing the factors and their respective powers

qn: 20(20) , 20(20) , 20(20) LCM

all expressions are equal, hence LCM will only be 20(20)= 400

tactic for solving LCM question: compare the factors of the given expression and their powers

just like in the image, it is the same tactic, in deriving the factors of the respective expressions first and multiplying the factors of the highest power together to get the lowest common multiple

working as explanation:

20(5)= 2²×5² × 3

20(10)= 2³×5² × 3

20(15)= 2²×3¹×5²

as shown in bold, the factor '3' only applies in the last expression and hence without taking in consideration of the fact that 3⁰=1 into the 1st 2 expression, it will be difficult to compare

now we focus on the factors and choose the highest powers of the factors, doesn't have to be common factor now but factors of the highest power will do:

20(5)= 2² × × 3⁰

20(10)= × × 3⁰

20(15)= 2² × × 5²

as shown in bold again, these are the factors that are the highest. all that we have to do now is to multiply them:

LCM = 2³×3¹×5²=600, also the answer in the image

hope this helps!

User He Shiming
by
2.9k points