Multiplying, dividing and mixed operations · Ages 9–10
Lowest (least) common multiple (L.C.M.) worksheet
Part of: Factors and multiples
In the print window, choose “Save as PDF” to download it. The answers print on the last page.
Lowest (least) common multiple (L.C.M.) worksheet
Multiplying, dividing and mixed operations · Ages 9–10
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.L.C.M. of 8 and 12 = ?
Answer:
2.L.C.M. of 5 and 7 = ?
Answer:
3.L.C.M. of 7 and 8 = ?
Answer:
4.L.C.M. of 15 and 9 = ?
Answer:
5.L.C.M. of 6 and 10 = ?
Answer:
6.L.C.M. of 6 and 8 = ?
Answer:
7.L.C.M. of 5 and 4 = ?
Answer:
8.L.C.M. of 13 and 4 = ?
Answer:
9.L.C.M. of 4 and 15 = ?
Answer:
10.L.C.M. of 5 and 8 = ?
Answer:
11.L.C.M. of 9 and 11 = ?
Answer:
12.L.C.M. of 15 and 10 = ?
Answer:
Part B: Word problems (4 marks each)
13.Lots of rectangular cards, 7 cm long and 5 cm wide, are fitted together with no gaps to make a square. All the cards face the same way. What is the shortest the square's side can be, in centimetres?
Working:
Answer:
14.Lots of rectangular cards, 12 cm long and 9 cm wide, are fitted together with no gaps to make a square. All the cards face the same way. What is the shortest the square's side can be, in centimetres?
Working:
Answer:
15.A box of sweets can be packed exactly into bags of 9, and also exactly into bags of 12. What is the smallest number of sweets the box can hold?
Working:
Answer:
16.Route A buses leave every 8 minutes and Route B buses every 10 minutes. Buses on both routes leave together at 8 a.m. In how many minutes will they next leave together?
Working:
Answer:
17.Route A buses leave every 9 minutes and Route B buses every 15 minutes. Buses on both routes leave together at 8 a.m. In how many minutes will they next leave together?
Working:
Answer:
18.May goes swimming every 5 days and Tsz-ching every 6 days. They both swim today. In how many days will they next swim on the same day?
Working:
Answer:
Show the answers and working
Lowest (least) common multiple (L.C.M.) worksheet: Answers and working
Part A: Working out and filling in
1. L.C.M. of 8 and 12 = 24
L.C.M. of 8 and 12: by short division, 8 and 12 ÷ 2 → 4 and 6; 4 and 6 ÷ 2 → 2 and 3; 2 and 3 share no factor but 1. Multiply the divisors and the last two numbers: 2 × 2 = 4, 4 × 2 = 8, 8 × 3 = 24, so the L.C.M. is 24
2. L.C.M. of 5 and 7 = 35
L.C.M. of 5 and 7: 5 and 7 share no factor but 1, so the L.C.M. is the two multiplied: 5 × 7 = 35
3. L.C.M. of 7 and 8 = 56
L.C.M. of 7 and 8: 7 and 8 share no factor but 1, so the L.C.M. is the two multiplied: 7 × 8 = 56
4. L.C.M. of 15 and 9 = 45
L.C.M. of 15 and 9: by short division, 15 and 9 ÷ 3 → 5 and 3; 5 and 3 share no factor but 1. Multiply the divisors and the last two numbers: 3 × 5 = 15, 15 × 3 = 45, so the L.C.M. is 45
5. L.C.M. of 6 and 10 = 30
L.C.M. of 6 and 10: by short division, 6 and 10 ÷ 2 → 3 and 5; 3 and 5 share no factor but 1. Multiply the divisors and the last two numbers: 2 × 3 = 6, 6 × 5 = 30, so the L.C.M. is 30
6. L.C.M. of 6 and 8 = 24
L.C.M. of 6 and 8: by short division, 6 and 8 ÷ 2 → 3 and 4; 3 and 4 share no factor but 1. Multiply the divisors and the last two numbers: 2 × 3 = 6, 6 × 4 = 24, so the L.C.M. is 24
7. L.C.M. of 5 and 4 = 20
L.C.M. of 5 and 4: 5 and 4 share no factor but 1, so the L.C.M. is the two multiplied: 5 × 4 = 20
8. L.C.M. of 13 and 4 = 52
L.C.M. of 13 and 4: 13 and 4 share no factor but 1, so the L.C.M. is the two multiplied: 13 × 4 = 52
9. L.C.M. of 4 and 15 = 60
L.C.M. of 4 and 15: 4 and 15 share no factor but 1, so the L.C.M. is the two multiplied: 4 × 15 = 60
10. L.C.M. of 5 and 8 = 40
L.C.M. of 5 and 8: 5 and 8 share no factor but 1, so the L.C.M. is the two multiplied: 5 × 8 = 40
11. L.C.M. of 9 and 11 = 99
L.C.M. of 9 and 11: 9 and 11 share no factor but 1, so the L.C.M. is the two multiplied: 9 × 11 = 99
12. L.C.M. of 15 and 10 = 30
L.C.M. of 15 and 10: by short division, 15 and 10 ÷ 5 → 3 and 2; 3 and 2 share no factor but 1. Multiply the divisors and the last two numbers: 5 × 3 = 15, 15 × 2 = 30, so the L.C.M. is 30
Part B: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. Lots of rectangular cards, 7 cm long and 5 cm wide, are fitted together with no gaps to make a square. All the cards face the same way. What is the shortest the square's side can be, in centimetres? (Answer: 35 cm)
The L.C.M. of 5 and 7 is 35
14. Lots of rectangular cards, 12 cm long and 9 cm wide, are fitted together with no gaps to make a square. All the cards face the same way. What is the shortest the square's side can be, in centimetres? (Answer: 36 cm)
The L.C.M. of 9 and 12 is 36
15. A box of sweets can be packed exactly into bags of 9, and also exactly into bags of 12. What is the smallest number of sweets the box can hold? (Answer: 36 sweets)
The L.C.M. of 9 and 12 is 36
16. Route A buses leave every 8 minutes and Route B buses every 10 minutes. Buses on both routes leave together at 8 a.m. In how many minutes will they next leave together? (Answer: 40 minutes)
The L.C.M. of 8 and 10 is 40
17. Route A buses leave every 9 minutes and Route B buses every 15 minutes. Buses on both routes leave together at 8 a.m. In how many minutes will they next leave together? (Answer: 45 minutes)
The L.C.M. of 9 and 15 is 45
18. May goes swimming every 5 days and Tsz-ching every 6 days. They both swim today. In how many days will they next swim on the same day? (Answer: 30 days)
The L.C.M. of 5 and 6 is 30
Numsprite · numsprite.com/en/worksheets/factors-and-multiples/lowest-common-multiple
Practise it in the gameLowest (least) common multiple (L.C.M.) · Unlimited questions, no download