The exercise is basically asking you to find the least common multiple of 32, 28 and 24.
In fact, by definition, that would be the first number that you will meet counting by 32s, 28s and 24s.
To start, we have to find the prime factorization of all the numbers:
[tex]32=2^5,\quad 28=2^2\cdot 7,\quad 2^3\cdot 3[/tex]
Now, we have to consider all primes appearing, i.e. 2, 3 and 7. If a prime appears in more than one number, we'll have to consider the highest exponent. So, the highest exponent of 2 is 5, while 3 and 7 only appear at the first power.
So, the least common multiple is
[tex]LCM(32,28,24)=2^5\cdot 3\cdot 7=672[/tex]
The distance (in feet) in which the three steps would overlap for the first time is 56 feet.
Using LCM method
We would find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.
Multiples of 24:
24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336, 360, 384, 408, 432, 456, 480, 504, 528, 552, 576, 600, 624, 648, 672, 696, 720
Multiples of 28:
28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308, 336, 364, 392, 420, 448, 476, 504, 532, 560, 588, 616, 644, 672, 700, 728
Multiples of 32:
32, 64, 96, 128, 160, 192, 224, 256, 288, 320, 352, 384, 416, 448, 480, 512, 544, 576, 608, 640, 672, 704, 736
Therefore,
LCM(24, 28, 32) = 672
Then we convert to feet:
672/12= 56 feet.
Read more about LCM here:
https://brainly.com/question/233244
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