17^22 - 1 is a multiple of :-
Answers
Answer:
17 and 22 LCM
In common notation: lcm (17,22) = 374.
Step-by-step explanation:
LCM of 17 and 22
The lcm of 17 and 22 is the smallest positive integer that divides the numbers 17 and 22 without a remainder. Spelled out, it is the least common multiple of 17 and 22. Here you can find the lcm of 17 and 22, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the lcm of 17 and 22, but also that of three or more integers including seventeen and twenty-two for example. Keep reading to learn everything about the lcm (17,22) and the terms related to it.
What is the LCM of 17 and 22
If you just want to know what is the least common multiple of 17 and 22, it is 374. Usually, this is written as
lcm(17,22) = 374
The lcm of 17 and 22 can be obtained like this:
The multiples of 17 are … , 357, 374, 391, ….
The multiples of 22 are …, 352, 374, 396, …
The common multiples of 17 and 22 are n x 374, intersecting the two sets above, n\neq 0 \thinspace\in\thinspace\mathbb{Z}n
=0∈Z.
In the intersection multiples of 17 ∩ multiples of 22 the least positive element is 374.
Therefore, the least common multiple of 17 and 22 is 374.
Taking the above into account you also know how to find all the common multiples of 17 and 22, not just the smallest. In the next section we show you how to calculate the lcm of seventeen and twenty-two by means of two more methods.
How to find the LCM of 17 and 22
The least common multiple of 17 and 22 can be computed by using the greatest common factor aka gcf of 17 and 22. This is the easiest approach:
lcm (17,22) = \frac{17 \times 22}{gcf(17,22)} = \frac{374}{1}
gcf(17,22)
17×22
=
1
374
= 374
Alternatively, the lcm of 17 and 22 can be found using the prime factorization of 17 and 22:
The prime factorization of 17 is: 17
The prime factorization of 22 is: 2 x 11
Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(17,17) = 374
In any case, the easiest way to compute the lcm of two numbers like 17 and 22 is by using our calculator below. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 17,22. Push the button only to start over.
Integers:
5,10,25,60,100
The lcm is...
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Use of LCM of 17 and 22
What is the least common multiple of 17 and 22 used for? Answer: It is helpful for adding and subtracting fractions like 1/17 and 1/22. Just multiply the dividends and divisors by 22 and 17, respectively, such that the divisors have the value of 374, the lcm of 17 and 22.
\frac{1}{17} + \frac{1}{22} = \frac{22}{374} + \frac{17}{374} = \frac{39}{374}
17
1
+
22
1
=
374
22
+
374
17
=
374
39
. \frac{1}{17} - \frac{1}{22} = \frac{22}{374} - \frac{17}{374} = \frac{5}{374}
17
1
−
22
1
=
374
22
−
374
17
=
374
5
.
Properties of LCM of 17 and 22
The most important properties of the lcm(17,22) are:
Commutative property: lcm(17,22) = lcm(22,17)
Associative property: lcm(17,22,n) = lcm(lcm(22,17),n) n\neq 0 \thinspace\in\thinspace\mathbb{Z}n
=0∈Z
The associativity is particularly useful to get the lcm of three or more numbers; our calculator makes use of it.
To sum up, the lcm of 17 and 22 is 374. In common notation: lcm (17,22) = 374.
If you have been searching for lcm 17 and 22 or lcm 17 22 then you have come to the correct page, too. The same is true if you typed lcm for 17 and 22 in your favorite search engine.
Note that you can find the least common multiple of many integer pairs including seventeen / twenty-two by using the search form in the sidebar of this page.
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