Cutting two planks with no waste
One length that fits both
Two planks of 24 cm and 36 cm are to be cut into equal pieces with nothing wasted.
📚 Chapter Learning Kit
Finding Common Ground · Class 7 Mathematics · Ganita Prakash
English 3 topics 105 leveled MCQs 51 flashcards 5 games Free
Shared by a Veda teacher · Generated with Veda AI · Oct 2026
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The numbers in both lists
Factors and common factors
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24, and those of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
The longest piece that works
The highest common factor
The carpenter wants the largest of those common factors, which is 12.
Every 6 minutes and every 8
Two bells ringing together
One bell rings every 6 minutes and another every 8, starting together.
The numbers in both lists
Multiples and common multiples
The multiples of 6 are 6, 12, 18, 24, 30 and so on, and those of 8 are 8, 16, 24, 32 and so on.
When they NEXT ring together
The lowest common multiple
The question asks for the smallest of the common multiples, which is 24.
📖 Smart notes
What you'll study, topic by topic
1
The highest common factor, by listing and by primes
A common factor divides both numbers, and the highest of them is the HCF. Listing works for small numbers; prime factorisation works for any, taking each shared prime the smaller number of times. Two numbers with HCF 1 a…
- A factor divides a number exactly, leaving nothing over.
- A common factor appears in both lists, and the highest is the HCF.
- The HCF of 24 and 36 is 12, by listing or by primes.
~40 min · full explanation, examples & memory tricks in the app
2
The lowest common multiple, and the larger count
A common multiple is divisible by both numbers, and the least of them is the LCM. There is no greatest, since the list never ends. By primes, take every prime at the LARGER count and keep the lone ones, the exact opposit…
- A multiple is a number times a whole number.
- A common multiple is divisible by both numbers, and the least is the LCM.
- The LCM of 6 and 8 is 24, so two such bells coincide every 24 minutes.
~40 min · full explanation, examples & memory tricks in the app
3
HCF times LCM, and a quicker procedure
The HCF multiplied by the LCM equals the two numbers multiplied, because each prime is taken at the smaller count and the larger, which add to the two counts. That gives a shortcut and a check. An HCF can also be found b…
- The HCF times the LCM equals the two numbers multiplied.
- For 20 and 30 that is 10 times 60, which matches 600.
- The HCF takes the smaller prime count and the LCM the larger.
~45 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
105 questions laddered from warm-up to topper-level, each with an explanation. A taste:
One number is divided by another and the division comes out with nothing left over at all. A factor of a number is one that
Beginner
A is smaller than it
B is a prime number
C adds to it exactly
D divides it exactly
Show answer & explanation
divides it exactly
Leaving nothing over.
Two planks of different lengths are to be cut into equal pieces with no wood wasted from either. That needs a piece length that
Beginner
A divides one of them exactly
B divides both exactly
C is the total of the two
D is the difference of the two
Show answer & explanation
divides both exactly
Which is a common factor.
The factors of 24 are
Beginner
A 1, 2, 3, 4, 6, 12 and 24
B 1, 2, 3, 4, 6, 8, 12 and 24
C 2, 3, 4, 6, 8 and 12
D 1, 2, 4, 8 and 24
Show answer & explanation
1, 2, 3, 4, 6, 8, 12 and 24
Each divides 24 exactly.
The factors of 36 are
Intermediate
A 1, 2, 3, 4, 6, 9, 12, 18 and 36
B 1, 2, 3, 4, 6, 12, 18 and 36
C 1, 2, 4, 9, 12 and 36
D 2, 3, 4, 6, 9, 12 and 18
Show answer & explanation
1, 2, 3, 4, 6, 9, 12, 18 and 36
Each divides 36 exactly.
🃏 Flashcards
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