  # Math - Age Problem

by Aleshia Hunter
(Logan, West Virginia, United States)

Demonstrate your understanding of the following terms by completing the exercise explained below:

• Prime Factorizations

• Least Common Multiple (LCM)

• Greatest Common Factor (GCF)

List:

2. The names and ages of two people you know

a) one person should be older than you

b) one person should be younger than you
(if you can, choose a person that is
at least 15 years your junior)

Find:

1. The prime factorization of each of the three ages
(Show the results by name and age)

Together, the three ages form a “set” of three numbers

2. Find the LCM for the set
(explain how you determined the LCM)

3. Find the GCF for the set
(explain how you determined the GCF)

In your own words, explain the following two concepts as they relate to the three ages. Explain the meaning of your calculations, not how you arrived at the numbers.

1. LCM

2. GCF

Ages Selected:

• Myself age 40
• Husband age 52
• nephew age 13

### Comments for Math - Age Problem

 Jan 04, 2012 LCM and GCF by: Staff ----------------------------------------------------------------------- Part III In your own words, explain the meaning of your calculated LCM and GCF for the ages you selected. LCM: The least common multiple of two or more numbers is three things: 1) first, a MULTIPLE; 2) second, a COMMON MULTIPLE; and 3) last, the LEAST OF ALL the possible COMMON MULTIPLES. There are many multiples for every number. There will be many common multiples for any two (or more) numbers. But, . . . there will be only one LCM. For example, some of the multiples of 2 are: 2 * 1 = 2 2 * 2 = 4 2 * 3 = 6 2 * 4 = 8 2 * 5 = 10 2 * 6 = 12 2 * 7 = 14 2 * 8 = 16 2 * 9 = 18 . . . Some of the multiples of 3 are: 3 * 1 = 3 3 * 2 = 6 3 * 3 = 9 3 * 4 = 12 3 * 5 = 15 3 * 6 = 18 3 * 7 = 21 . . . In this example, the multiples of 2 which are listed are: 2 4 6 8 10 12 14 16 18 . . . And the multiples of 3 which are listed are: 3 6 9 12 15 18 21 . . . Some of the multiples of 2 are the same as some of the multiples of 3. The multiples of 6, 12, and 18 appear in both lists. 6, 12, and 18 are some of the COMMON MULTIPLES for the numbers 2 and 3 The LCM is the smallest of the common multiples (the smallest of the numbers 6, 12, and 18). LCM = 6 GCF: The greatest common factor of two or more numbers is three things: 1) first, a FACTOR; 2) second, a COMMON FACTOR; and 3) last, the GREATEST OF ALL the COMMON FACTORS. There may be many factors for every number. There may be many common factors for any two (or more) numbers. But, . . . there will be only one GCF. For example, factors of 48 are: 2 * 2 * 2 * 2 * 3 = 48 The factors of 32 are: 2 * 2 * 2 * 2 * 2 = 32 So, the factors of 48 are can be written: 48 = 2⁴ * 3 48 = 16 * 3 And the factors of 32 can be written: 32 = 2⁴ * 2 32 = 16 * 2 The number 16 is a factor. The number 16 is a common factor (not a prime factor). It appears as a factor for both 48 and 32. 16 is the largest common factor which appears as a factor for both 48 and 32. GCF = 16 Thanks for writing. Staff www.solving-math-problems.com

 Jan 04, 2012 LCM and GCF by: Staff ----------------------------------------------------------------------- Part II You can also find the GCF (greatest common factor) using the same prime factors which you used to compute the LCM. Myself age: 40, factors = 1 * 2 * 2 * 2 * 5 Husband age: 52, factors = 1 * 2 * 2 * 13 Nephew age: 13, factors = 1 * 13 Which factors appear as a prime factor for all three ages? There is only one number which appears as one of the prime numbers for all three ages: 1 GCF (for the numbers 40, 52, and 13) = 1 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Parenthetical Note: The particular ages you selected don’t provide a good, general example which can be used to demonstrate how to find the GCF To demonstrate the process for finding the GCF, I have chosen three other numbers: 10, 75, and 20 10, factors = 2 * 5 = 2¹ * 5¹ 75, factors = 3 * 5 * 5 = 3¹ * 5² 20, factors = 2 * 2 * 5 = 2² * 5¹ How many times is the number 2 listed for each number? First Number: 10, prime factors = 2¹ * 5¹ 2 is listed 1 time Second Number: 75, prime factors = 3¹ * 5² 2 is listed 0 (zero) times Third Number: 20, prime factors = 2² * 5¹ 2 is listed 2 times How many times is the number 5 listed for each number? First Number: 10, prime factors = 2¹ * 5¹ 5 is listed 1 time Second Number: 75, prime factors = 3¹ * 5² 5 is listed 2 times Third Number: 20, prime factors = 2² * 5¹ 5 is listed 1 time How many times is the number 3 listed for each number? First Number: 10, prime factors = 2¹ * 5¹ 3 is listed 0 (zero) times Second Number: 75, prime factors = 3¹ * 5² 3 is listed 1 time Third Number: 20, prime factors = 2² * 5¹ 3 is listed 0 (zero) times Since the 2 and the 3 are not listed as a factor for all three numbers, they are NOT common factors. ONLY 5 is a common factor Pick the lowest number of times five is listed. The number 5 is listed one time as a prime factor for all three numbers. (Although 5 is listed twice as a prime factor for the number 75, it is not listed twice for 10 or 20.) GCF (for the numbers 10, 75, and 20) = 5 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: -----------------------------------------------------------------------