Lesson 57: Finding the Least Common Multiple — Practice Questions

1. 1. What is the Least Common Multiple (LCM) of the monomials $6ab^2$ and $8a^3b$? The LCM is ___.

2. 2. What is the LCM of the monomials $10x^3y^2$ and $15xz^4$?

   • A. $30x^3y^2z^4$
   • B. 5x
   • C. $30x^3y^2$
   • D. $150x^4y^2z^4$

3. 3. Find the LCM of the polynomials $(6x^2 - 12x)$ and $(9x - 18)$. The LCM is ___.

4. 4. What is the LCM of the polynomials $y^2 - 9$ and $y^2 - 6y + 9$?

   • A. (y+3)(y-3)
   • B. $(y-3)^2$
   • C. $(y+3)(y-3)^2$
   • D. $(y^2-9)(y^2-6y+9)$

5. 5. If two polynomials are factored as $P_1 = (x+1)^3(x-2)$ and $P_2 = (x+1)(x+4)^2$, what is their LCM?

   • A. $(x+1)^3(x-2)(x+4)^2$
   • B. (x+1)(x-2)(x+4)
   • C. $(x+1)^4(x-2)(x+4)^2$
   • D. (x+1)

6. 6. What is the Least Common Multiple (LCM) of 14 and 21? The answer is ___.

7. 7. The prime factorization of 24 is $2^3 \cdot 3$ and for 36 is $2^2 \cdot 3^2$. Which expression represents the LCM of 24 and 36?

   • A. $2^2 \cdot 3$
   • B. $2^3 \cdot 3^2$
   • C. $2^5 \cdot 3^3$
   • D. $2 \cdot 3$

8. 8. Find the Least Common Multiple (LCM) of 10, 15, and 25. The LCM is ___.

9. 9. Two lights flash at the same time. One flashes every 8 seconds, and the other flashes every 10 seconds. After how many seconds will they next flash together?

   • A. 2 seconds
   • B. 18 seconds
   • C. 40 seconds
   • D. 80 seconds

10. 10. What is the Least Common Multiple (LCM) of 40 and 50?

    • A. 10
    • B. 90
    • C. 200
    • D. 2000