Question

Determine if you should find the LCM or GCF Boxes that are 12 inches t

Factors and multiples
ANSWERED
asked 2021-08-08
Determine if you should find the LCM or GCF Boxes that are 12 inches tall are being stacked next to boxes that are 18 inches tall. What is the shortest height at which the two stacks will be the same height? Do it right LCM- least common multiple GCF- greatest common factor.
1) GCF NS 2) LCM

Answers (1)

2021-08-09
Step 1
We are given in the question that:
Boxes which are 12 inches tall are being stacked next to 18 inches tall boxes.
Now :
We have to determine :
The shortest height at which the two stacks will be of same height:
So, we know
18 inches tall boxes can have the stack of heights 18 inch, 36 inch, 54 inch, 72 inch, 90 inch etc.
It can not be shorter of its height.
Step 2
Similarly,
12 inches tall boxes can have the stack of heights 12 inch, 24 inch, 36 inch, 48 inch, 60 inch etc.
It can not be shorter of its height also.
Hence,
We should find LCM (Least Common Multiple) here, as we can take the multiples for both (18 inches and 12 inches tall boxes), because boxes can not be stacked shorter of their heights, so we don't need to find Greatest Common Factor here.
Hence,
Multiples for \(\displaystyle{18}={18},{36},{54},{72},{90}\)
Multiples for \(\displaystyle{12}={12},{24},{36},{48},{60}\)
Hence both have 36 common as the least multiple.
Step 3
Hence, 2 boxes of 18 inches and 3 boxes of 12 inches can be stacked together to get the two stacks at the same height i.e. 36 cm.
So , The shortest height at which both boxes are stacked together is 36 cm.
So,
LCM- is the correct answer.
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