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prime factorizations, lcm and gcf of numbers 43, 20, and 57











































Given the following three numbers: 43, 20, 57

Compute:

1. Prime Factorizations

2. LCM (least common multiple)

3. GCF (greatest common factor)

Comments for prime factorizations, lcm and gcf of numbers 43, 20, and 57

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Jul 05, 2012
Prime Factorizations, LCM and GCF
by: Staff


The answer:


1. Prime Factorizations


Prime Factorization means to find all the prime factors

A Prime Factor is a positive integer (or natural number, if you prefer) which is:

- greater than 1
- cannot be divided by any positive integer other than itself and the number 1

It is worth noting that the number 1 is not a prime factor.


43 = 1 * 43

43 is a prime number

>>> The prime factorization of 43 = 43


20 = 2 * 2 * 5

20 = 2² * 5

2 and 5 are prime numbers

>>> The prime factorization of 20 = 2 * 2 * 5


57 = 3 * 19

3 and 19 are prime numbers

>>> The prime factorization of 57 = 3 * 19



2. Least Common Multiple (LCM) of 43, 20, and 57

You can find the LCM (least common multiple) using the factors which you have already computed

List the prime factors again, being careful to show the exponents associated with each:

43, prime factors = 43¹

20, prime factors = 2² * 5¹

57, prime factors = 3¹ * 19¹

All together, there are the five different prime factors listed: 43, 2, 5, 3, and 19


To compute the LCM:

Choose the 43 with the highest exponent: 43¹

Choose the 2 with the highest exponent: 2²

Choose the 5 with the highest exponent: 5¹

Choose the 3 with the highest exponent: 3¹

Choose the 19 with the highest exponent: 19¹


Multiply all five of these numbers together


LCM = 43¹ * 2² * 5¹ * 3¹ * 19¹ = 49020

>>> LCM (least common multiple) for the values 43, 20, and 57 = 49020



3. Greatest Common Factors (GCF)

You can also find the GCF (greatest common factor) using the factors you have already computed.

43 = 1 * 43

20 = 1 * 2 * 2 * 5

57 = 1 * 3 * 19


Which factors appear as a factor for all three numbers?

1

1 is the only number which appears as one of the factors for all three numbers.

>>> GCF (for the numbers 43, 20, and 57) = 1



Thanks for writing.

Staff
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