Least, but not last
The smallest length that two kinds of pieces can both make.
Two torans, one length
Anshu stitches a toran from strips of 6 cm. Guna uses strips of 8 cm. They want torans of the same length.
What is the shortest toran that both of them can make?
What this lesson covers
The idea
The Lowest Common Multiple (LCM) of two or more numbers is the lowest (smallest or least) of their common multiples.
Two torans, one length
Anshu stitches a toran from strips of 6 cm. Guna uses strips of 8 cm. They want torans of the same length.
What is the shortest toran that both of them can make?
- 12 cm
- 24 cm
- 48 cm
Make the bars match
Add pieces to each bar. When both bars end together, the length goes on the shelf. Find the shortest length that matches.
The lowest common multiple
Any toran Anshu makes is a multiple of 6. Any toran Guna makes is a multiple of 8. A length that both can make is a common multiple.
24 is the smallest common multiple. There is no largest one: after 48 come 72, 96, … without end.
The Lowest Common Multiple (LCM) of two or more numbers is the lowest (smallest or least) of their common multiples.
- Who | Lengths (cm)
- Anshu | 6, 12, 18, 24, 30, 36, 42, 48, …
- Guna | 8, 16, 24, 32, 40, 48, 56, …
- Both | 24, 48, …
Notes
The Lowest Common Multiple (LCM) of two or more numbers is the lowest (smallest or least) of their common multiples.
Check yourself
One bell rings every 9 minutes and another every 12 minutes. They ring together at time 0. After how many minutes do they next ring together?
Answer: 36 min
Multiples of 9: 9, 18, 27, 36. Multiples of 12: 12, 24, 36. The first common one is 36 minutes.
Which number is a common multiple of 6 and 8, but not the lowest one?
Is there a largest common multiple of 6 and 8?
Find the LCM of 7 and 11.
Answer: 77
7 and 11 share no factor, so the first common multiple is 7 × 11 = 77.
- 18. 18 is a multiple of 6, but not of 8.
- 24. 24 is a common multiple, and it is the lowest: this is the LCM.
- 48 — correct. Yes! 48 = 6 × 8 = 8 × 6 is a common multiple, but 24 is lower.
- No: the list 24, 48, 72, 96, … never ends. — correct. Yes! Every multiple of 24 is also a common multiple, so we can always find a bigger one.
- Yes: 48. 72 is a common multiple that is bigger than 48.
- Yes: 24. 24 is the lowest common multiple. The common multiples go on after it.