MHB Common Multiple, what is the fourth term

  • Thread starter Thread starter Yazan975
  • Start date Start date
  • Tags Tags
    Multiple Term
Click For Summary
SUMMARY

The discussion centers on finding the fourth term in a set of algebraic expressions to achieve a specific least common multiple (LCM). The given terms are 12a²bc, 8ab, and 4a²cd, with their LCM calculated as 24a²bcd. To reach the desired LCM of 24a³bc²d, an additional term must contribute one more 'a' and one more 'c'. The coefficient of this new term must be an odd prime number that divides 24, which is determined to be 3.

PREREQUISITES
  • Understanding of least common multiples (LCM)
  • Familiarity with algebraic expressions and coefficients
  • Knowledge of prime numbers and their properties
  • Basic skills in manipulating algebraic terms
NEXT STEPS
  • Research how to calculate the least common multiple of algebraic expressions
  • Study the properties of prime numbers and their role in factorization
  • Learn about algebraic manipulation techniques for combining terms
  • Explore examples of finding LCM in polynomial expressions
USEFUL FOR

Students studying algebra, mathematicians working with polynomial expressions, and educators teaching LCM concepts in mathematics.

Yazan975
Messages
30
Reaction score
0

Attachments

  • Chpt2.2-min.png
    Chpt2.2-min.png
    131.6 KB · Views: 106
Mathematics news on Phys.org
Can you show what you've tried or your thoughts on how to begin?
 
Three of the terms are 12a^2bc, 8ab, and 4a^2cd. To find the least common multiple of those 3, note that 12= 2^2(3), 8= 2^3, and 4= 2^2. The least common multiple of those three is 2^3(3)= 24. The highest power of a is a^2 and the highest power of b, c, and d is 1 for all three. So the least common multiple of those three terms is 24a^2bcd. We want another term such that the least common multiple of all four terms is 24a^3bc^2d. We already have the "24", the "b" and "d", two of the three "a"s, and one of the two "c"s. It looks like we need just one more "a" and one more "c". Any coefficient must be already included in the "24". What is an odd prime number that divides 24?
 
Last edited:

Similar threads

High School How to prove this for every Arithmetic Progression?
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Formal definition of multiplication for real and complex numbers
  • · Replies 2 ·
Replies
2
Views
2K
High School What is the link between proportion and multiplication?
  • · Replies 3 ·
Replies
3
Views
2K
MHB 13.3.2 What is the 50th term of the sequence
  • · Replies 3 ·
Replies
3
Views
2K
High School A question about rules of multiplication
  • · Replies 4 ·
Replies
4
Views
2K
High School Sine Multiplication
  • · Replies 5 ·
Replies
5
Views
2K
High School Are there two kinds of inverse with respect to closure?
  • · Replies 18 ·
Replies
18
Views
2K
Undergrad Method for finding a complex series?
  • · Replies 10 ·
Replies
10
Views
2K
High School About a definition: What is the number of terms of a polynomial P(x)?
  • · Replies 48 ·
2
Replies
48
Views
4K
High School Relation between Division and multiplication
  • · Replies 50 ·
2
Replies
50
Views
5K