What is LCM of Monomials? | Simple Explanation for Class 7

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What is the Lowest Common Multiple (LCM) of Monomials?

Grade Level:

Class 7

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The Lowest Common Multiple (LCM) of Monomials is the smallest monomial that can be divided evenly by all the given monomials. It's like finding the smallest common ground for different algebraic expressions.

Simple Example

Quick Example

Imagine you have two friends, Rohan who buys a new cricket bat every '2x' months and Priya who buys one every '3y' months. To find when they both buy a new bat at the same time, we'd look for the LCM of '2x' and '3y'. The LCM would be '6xy' months, meaning after 6xy months, they both would have bought a new bat.

Worked Example

Step-by-Step

Let's find the LCM of 6x^2y and 9xy^3.

Step 1: Find the LCM of the numerical coefficients.
LCM of 6 and 9 is 18.

---Step 2: Identify all unique variables present in the monomials.
Here, the variables are x and y.

---Step 3: For each variable, pick the highest power it has in any of the monomials.
For x, the powers are x^2 and x^1. The highest power is x^2.
For y, the powers are y^1 and y^3. The highest power is y^3.

---Step 4: Multiply the LCM of the coefficients by the variables with their highest powers.
LCM = (LCM of coefficients) * (highest power of x) * (highest power of y)
LCM = 18 * x^2 * y^3

---Answer: The LCM of 6x^2y and 9xy^3 is 18x^2y^3.

Why It Matters

Understanding LCM of monomials helps you simplify complex equations in Physics or solve problems in Engineering. It's a foundational skill for Computer Science and even helps in understanding algorithms used in AI/ML, making you a problem-solver for future tech challenges.

Common Mistakes

MISTAKE: Finding the HCF (Highest Common Factor) of coefficients instead of LCM. | CORRECTION: Always find the LCM of the numerical coefficients, not the HCF.

MISTAKE: Picking the lowest power of a variable instead of the highest. For example, taking x^1 instead of x^2. | CORRECTION: For LCM, always choose the highest power of each variable present in any of the monomials.

MISTAKE: Forgetting to include a variable that appears in only one monomial. | CORRECTION: Include all unique variables present in any of the monomials, even if they appear in only one, using their highest power.

Practice Questions

Try It Yourself

QUESTION: Find the LCM of 4a and 8a^2. | ANSWER: 8a^2

QUESTION: What is the LCM of 5x^2y and 10xy^2z? | ANSWER: 10x^2y^2z

QUESTION: Find the LCM of 3p^3q, 6pq^2, and 9p^2q^3. | ANSWER: 18p^3q^3

MCQ

Quick Quiz

Which of the following is the LCM of 7m^2n and 14mn^3?

7mn

14m^2n^3

14mn^3

7m^2n^3

The Correct Answer Is:

The LCM of 7 and 14 is 14. For 'm', the highest power is m^2. For 'n', the highest power is n^3. So, the LCM is 14m^2n^3.

Real World Connection

In the Real World

Imagine you are programming a traffic light system in a smart city. If light A turns green every '3x' seconds and light B turns green every '5y' seconds, finding their LCM (15xy seconds) helps synchronize them to prevent traffic jams. This concept is used by engineers at companies like Siemens or Bosch developing smart city solutions.

Key Vocabulary

Key Terms

MONOMIAL: An algebraic expression with only one term, like 5x or 3y^2 | COEFFICIENT: The numerical part of a monomial, like 5 in 5x | VARIABLE: A letter representing an unknown value, like x or y | POWER (EXPONENT): The small number written above a base, showing how many times the base is multiplied by itself, like 2 in x^2

What's Next

What to Learn Next

Great job learning about LCM of Monomials! Next, you can explore the Highest Common Factor (HCF) of Monomials. It's a related concept that will further strengthen your understanding of algebraic expressions and help you simplify them even more.