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

 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 www.solving-math-problems.com