Question

Find the greatest length which can be contained exactly in 10 m, 5 dm, 2 cm, 4 mm and 12 mm, 7 dm, 5 cm, 2 mm.

Answer 1

Hint: We have to convert the above measurements to the smallest units in the question. Convert each and every measurement seperately.

Complete step-by-step answer:
Step - 1: Convert the measurements to the smallest units.
The smallest unit is mm.
The conversions are as follows:
1 m = 1000 mm
1 cm = 10 mm
1 dm = 100 mm
Step – 2: Appling the conversions in the given measurements.
We have;
10m, 5dm, 2cm, 4mm
We know that;
1 m = 1000 mm
Then, 10 X 1000 = 10000mm
Again, we know that;
1 dm = 100 mm
Then, 5 X 100 = 500mm
Again, we know that;
1 cm = 10 mm
Then, 2 X 10 = 20mm
And 4 is already the smallest unit that is 4 mm.
Adding all the lengths together = 10000 + 500 + 20 + 4 = 10524 mm
Again, we have lengths;
12 m, 7 dm, 5 cm, 2 mm
We know that;
1 m = 1000 mm
$ \Rightarrow $12 X 1000 = 12000 mm
Again, we know that;
1 dm = 100 mm
$ \Rightarrow $7 X 100 = 700 mm
Again, we know that;
1 cm = 10 mm
$ \Rightarrow $5 X 10 = 50 mm
And 2 mm is already is in smallest unit.
Adding all the lengths, we have;
Sum of all the lengths = 12000 mm + 700 mm + 50 mm + 2 mm = 12752 mm
Step – 3: Get the GCD of the two measurements by prime factorization.
12752 = 2 X 2 X 2 X 2 X 797
10524 = 2 X 2 X 3 X 877
As we can see that 2 X 2 is common prime factors in 12752 and 10524.
Thus, GCD = ${2^2} = 4mm$

Therefore, the greatest length that can be contained exactly in the two measurements is 4 mm.

Note: The greatest common divisor (GCD), also called the greatest common factor, of two numbers is the largest number that divides them both. The GCD of several numbers may be computed by simply listing the factors of each number and determining the largest common one.