LCM by Division Method Worksheet

Welcome to your LCM by Division Method Worksheet! This worksheet will guide you through the process of finding the Least Common Multiple (LCM) using the division method. Practice with the provided exercises to enhance your understanding of this important mathematical concept.

Exercise 1: Finding the LCM

Find the LCM of the following pairs of numbers using the division method:

1. 18 and 24
2. 30 and 45
3. 36 and 48

Solution:

1. 18 and 24

   • Prime factorization of 18: $2\times 3^2$
   • Prime factorization of 24: $2^3\times 3$
   • Build LCM:
     • The highest power of 2: $2^3$
     • The highest power of 3: $3^2$
   • LCM: $2^3\times 3^2=72$

2. 30 and 45

   • Prime factorization of 30: $2\times 3\times 5$
   • Prime factorization of 45: $3^2\times 5$
   • Build LCM:
     • The highest power of 2: $2^1$
     • The highest power of 3: $3^2$
     • The highest power of 5: $5^1$
   • LCM: $2^1\times 3^2\times 5^1=90$

3. 36 and 48

   • Prime factorization of 36: $2^2\times 3^2$
   • Prime factorization of 48: $2^4\times 3$
   • Build LCM:
     • The highest power of 2: $2^4$
     • The highest power of 3: $3^2$
   • LCM: $2^4\times 3^2=144$

Exercise 2: Challenge Problems

Solve these more complex LCM problems using the division method:

1. Find the LCM of 15, 20, and 25.
2. Determine the LCM of 72, 90, and 120.

Solution:

1. 15, 20, and 25

   • Prime factorization of 15: $3\times 5$
   • Prime factorization of 20: $2^2\times 5$
   • Prime factorization of 25: $5^2$
   • Build LCM:
     • The highest power of 2: $2^2$
     • The highest power of 3: $3^1$
     • The highest power of 5: $5^2$
   • LCM: $2^2\times 3^1\times 5^2=300$

2. 72, 90, and 120

   • Prime factorization of 72: $2^3\times 3^2$
   • Prime factorization of 90: $2\times 3^2\times 5$
   • Prime factorization of 120: $2^3\times 3\times 5$
   • Build LCM:
     • The highest power of 2: $2^3$
     • The highest power of 3: $3^2$
     • The highest power of 5: $5^1$
   • LCM: $2^3\times 3^2\times 5^1=360$

Conclusion

Congratulations! You've successfully tackled LCM problems using the division method. Keep practicing to refine your skills and enhance your problem-solving abilities. Understanding LCM is an important step toward becoming a confident and capable mathematician.