Practice Solving LCM Word Problems (With Answer Key)

on

Understanding how to calculate the Lowest Common Multiple (LCM) is one thing, but applying it to solve real-life scenarios can be tricky! This page focuses specifically on LCM word problems to help you practice identifying when and how to use LCM.

Read each problem carefully and try to find the solution. If you need help calculating the LCM itself, remember our LCM Calculator Tool is available. An answer key is provided at the end to help you verify your final answers.

LCM Word Problems for Practice

  1. Two buses, Route A and Route B, start from the same bus stop at 8:00 AM. Route A completes its round trip and returns to the stop every 25 minutes. Route B completes its round trip every 35 minutes. At what time will they next arrive back at the bus stop *together*?
  2. Maria is buying supplies for a party. Juice boxes come in packs of 6, and snack bags come in packs of 8. What is the smallest number of juice boxes and snack bags she needs to buy to have exactly the same number of each?
  3. Find the smallest 4-digit number which is exactly divisible by 12, 15, and 18.
  4. Sam has drum lessons every 5 days and guitar lessons every 4 days. If he had both lessons today, how many days will pass before he has both lessons on the same day again?
  5. What is the least number of identical square marble tiles required to pave a rectangular courtyard measuring 20 meters by 16 meters? (Careful! This is a classic HCF problem about the *size* of the largest tile. Let's rephrase for LCM) -> **Revised 5:** What is the side length of the smallest square area that can be completely covered by rectangular posters of size 20 inches x 1 inch and also by posters of size 16 inches x 1 inch?
  6. Three runners start running around a circular track of length 400m from the same point at the same time. Their speeds are 2 m/s, 4 m/s and 5 m/s. When will they meet again at the starting point for the first time?
  7. A shopkeeper sells candles in packets of 12 and candle stands in packets of 8. What is the least number of packets of each that should be bought so that there is one candle for each candle stand?
  8. Find the smallest number which when divided by 20, 25, and 30 leaves a remainder of 5 in each case.
  9. Two different pieces of music have lengths of 48 seconds and 60 seconds. If both pieces start playing at the same time on repeat, after how many seconds will they start together again?
  10. What is the minimum volume (in cubic cm) of a cubical box that can be completely filled with identical rectangular bricks measuring 10 cm x 8 cm x 6 cm?
  11. Jessica visits her grandmother every 14 days. Her cousin, Mark, visits the same grandmother every 21 days. If they both visited today, in how many days will they next visit on the very same day?
  12. A bakery sells muffins in boxes of 4 and donuts in boxes of 6. What is the smallest number of muffins and donuts the bakery must sell to have sold the same quantity of each item?

Answer Key for Word Problems

Check your final answers here. Use the calculator link above if you need help with the LCM calculations.

  1. LCM(25, 35) = 175 minutes. They arrive together after 175 mins (2 hours 55 mins). Time: 8:00 AM + 2h 55m = 10:55 AM.
  2. LCM(6, 8) = 24. She needs to buy enough packs to get 24 juice boxes and 24 snack bags.
  3. LCM(12, 15, 18) = 180. Multiples of 180: 180, 360, 540, 720, 900, 1080... Smallest 4-digit number is 1080.
  4. LCM(5, 4) = 20 days.
  5. LCM(20, 16) = 80. The side length is 80 inches.
  6. Time = Dist/Speed. Runner 1: 400/2=200s. Runner 2: 400/4=100s. Runner 3: 400/5=80s. Find LCM(200, 100, 80). LCM = 400 seconds.
  7. LCM(12, 8) = 24. Need 24 candles and 24 stands. Packets of candles: 24/12=2. Packets of stands: 24/8=3. Answer: 2 packets of candles and 3 packets of stands.
  8. LCM(20, 25, 30) = 300. Number = 300 + 5 = 305.
  9. LCM(48, 60) = 240. They start together again after 240 seconds (or 4 minutes).
  10. The side of the cubical box must be a multiple of 10, 8, and 6. Find LCM(10, 8, 6) = 120. The side length is 120 cm. Volume = side³ = 120³ = 1,728,000 cubic cm.
  11. LCM(14, 21) = 42 days.
  12. LCM(4, 6) = 12. Smallest number of each item is 12 muffins and 12 donuts.

Apply LCM Concepts with Confidence!

Working through these LCM word problems helps you translate real-world situations into mathematical terms. Keep practicing! And don't forget, our LCM Calculator Tool is ready to assist with the core calculations.

Comments

Post a Comment