Calculate the number of irreducible proper fractions
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189. $A = EKOB(36; 60; 84)$ olarsa, məxrəci A olan ixtisar olunmayan düzgün kəsrlərin sayını tapın. A) 36 B) 72 C) 144 D) 288 E) 576
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Hi Yusif, let's solve this problem together. We need to find the number of irreducible proper fractions with a denominator equal to the least common multiple of 36, 60, and 84.
Problem Setup
First, let's find the least common multiple, or LCM, of the numbers 36, 60, and 84 by prime factorizing them.
To get the LCM, we take each prime factor raised to its highest power present in these factorizations.
Calculating this, we have 4 times 9 times 5 times 7, which equals 1260.
Now, we need to find how many proper fractions with denominator 1260 are irreducible. A fraction is irreducible if the numerator and denominator share no common factors.
Counting Irreducible Fractions
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