LCM Practice Quiz: The Ultimate LCM Practice Quiz – Concepts, Problems & Applications

12 = 2 squared times 3 and 16 = 2 to the power 4. LCM = 2 to the power 4 times 3 = 48 minutes. Option A gives 32, not a multiple of 12. Option B gives 36, not a multiple of 16. Option D gives 96, which is a common multiple but not the lowest. Only 48 is the smallest number divisible by both 12 and 16.

25 = 5 squared and 40 = 2 cubed times 5. LCM = 2 cubed times 5 squared = 8 times 25 = 200. Option A gives 100, not a multiple of 40 — wait, 100 divided by 40 = 2.5, not an integer. Option B gives 150, not a multiple of 40. Option D gives 250, not a multiple of 40. Only 200 is divisible by both 25 and 40.

The answer is True. Two distinct prime numbers share no common factors other than 1. When numbers share no common factors their LCM equals their product. For example LCM(3,7) = 21 = 3 times 7, and LCM(5,11) = 55 = 5 times 11. This rule applies to any two distinct primes without exception.

36 = 2 squared times 3 squared and 54 = 2 times 3 cubed. LCM = 2 squared times 3 cubed = 4 times 27 = 108. Option A gives 72, not a multiple of 54. Option B gives 144, which is a common multiple but not the lowest. Option D gives 162, not a multiple of 36. Only 108 is the smallest number divisible by both 36 and 54.

45 = 3 squared times 5 and 60 = 2 squared times 3 times 5. LCM = 2 squared times 3 squared times 5 = 4 times 9 times 5 = 180. Option B gives 270, not a multiple of 60. Option C gives 360, which is a common multiple but not the lowest. Option D gives 540, also not the lowest. Only 180 is the smallest number divisible by both 45 and 60.

22 = 2 times 11 and 44 = 2 squared times 11. LCM = 2 squared times 11 = 44. Since 44 is already a multiple of 22, the LCM is simply 44. Option A gives 22, which is not a multiple of 44. Option B gives 66, not a multiple of 44. Option D gives 88, which is a common multiple but not the lowest.

16 = 2 to the power 4 and 18 = 2 times 3 squared. LCM = 2 to the power 4 times 3 squared = 16 times 9 = 144. Option A gives 32, not a multiple of 18. Option B gives 48, not a multiple of 18. Option D gives 180, which is a common multiple but not the lowest. Only 144 is the smallest number divisible by both 16 and 18.

20 = 2 squared times 5 and 28 = 2 squared times 7. LCM = 2 squared times 5 times 7 = 140. Option A gives 80, not a multiple of 7. Option C gives 160, not a multiple of 7. Option D gives 200, not a multiple of 7. Only 140 is divisible by both 20 and 28.

14 = 2 times 7 and 21 = 3 times 7. LCM = 2 times 3 times 7 = 42 minutes. Option A gives 21, not a multiple of 14. Option C gives 63, not a multiple of 14. Option D gives 84, which is a common multiple but not the lowest. Only 42 is the smallest number divisible by both 14 and 21.

6 = 2 times 3 and 9 = 3 squared. LCM = 2 times 3 squared = 18 hours. Option B gives 24, not a multiple of 9. Option C gives 30, not a multiple of 9. Option D gives 36, which is a common multiple but not the lowest. Only 18 is the smallest number divisible by both 6 and 9.

Since 3 and 5 share no common factors, LCM = 3 times 5 = 15. Option A gives 10, which is not a multiple of 3. Option C gives 20, not a multiple of 3. Option D gives 25, not a multiple of 3. Only 15 is divisible by both 3 and 5.

28 = 2 squared times 7 and 42 = 2 times 3 times 7. LCM = 2 squared times 3 times 7 = 84 minutes. Option B gives 96, not a multiple of 7. Option C gives 112, not a multiple of 42. Option D gives 126, which is a common multiple but not the lowest. Only 84 is the smallest number divisible by both 28 and 42.

6 = 2 times 3 and 8 = 2 cubed. LCM = 2 cubed times 3 = 24. Option A gives 12, not a multiple of 8. Option C gives 30, not a multiple of 6 or 8. Option D gives 48, which is a common multiple but not the lowest. Only 24 is the smallest number divisible by both 6 and 8.

8 = 2 cubed and 12 = 2 squared times 3. LCM = 2 cubed times 3 = 24 seconds. Option B gives 30, not a multiple of 8. Option C gives 36, not a multiple of 8. Option D gives 38, not a multiple of 8 or 12. Both lights change together after 24 seconds.

10 = 2 times 5 and 15 = 3 times 5. LCM = 2 times 3 times 5 = 30 minutes. Option A gives 20, not a multiple of 15. Option C gives 40, not a multiple of 15. Option D gives 50, not a multiple of 15. Both bells ring together every 30 minutes.

2 = 2 and 9 = 3 squared. Since they share no common factors, LCM = 2 times 9 = 18. Option A gives 9, not a multiple of 2. Option B gives 12, not a multiple of 9. Option D gives 36, which is a common multiple but not the lowest. Only 18 is the smallest number divisible by both 2 and 9.

8 = 2 cubed and 14 = 2 times 7. LCM = 2 cubed times 7 = 8 times 7 = 56. Option A gives 28, not a multiple of 8. Option B gives 32, not a multiple of 7. Option D gives 84, which is a common multiple but not the lowest. Only 56 is the smallest number divisible by both 8 and 14.

9 = 3 squared and 12 = 2 squared times 3. LCM = 2 squared times 3 squared = 4 times 9 = 36. Option A gives 27, not a multiple of 12. Option C gives 45, not a multiple of 12. Option D gives 18, not a multiple of 12. Only 36 is divisible by both 9 and 12.

4 = 2 squared and 6 = 2 times 3. LCM takes the highest power of each prime: 2 squared times 3 = 12. Option A gives 6, which is not a multiple of 4. Option B gives 8, not a multiple of 6. Option D gives 10, not a multiple of 4 or 6. Only 12 is divisible by both 4 and 6.

Since 7 and 3 share no common factors, LCM = 7 times 3 = 21. Option A gives 13, which is not a multiple of 7 or 3. Option C gives 28, not a multiple of 3. Option D gives 35, not a multiple of 3. Only 21 is divisible by both 7 and 3.