HCF and LCM
The highest common factor (HCF) is the biggest number that divides into both numbers. The lowest common multiple (LCM) is the smallest number both go into.
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Analogy
HCF is the biggest tile that fits both floors. LCM is when two buses next meet at the stop.
Example
36 = 2^2 x 3^260 = 2^2 x 3 x 5HCF = 2^2 x 3 = 12LCM = 2^2 x 3^2 x 5 = 180
In practice
Two buses leaving every 12 and 15 minutes line up again after 60 minutes, the LCM.
Practice
Flashcards
- What is the HCF of 36 and 60?12. It is the biggest number that divides into both.
Interview questions
- Write 36 and 60 as products of prime factors, then find their HCF and LCM.
- 36 = 2^2 x 3^2
- 60 = 2^2 x 3 x 5
- HCF uses shared primes with smaller powers: 12
- LCM uses every prime with larger powers: 180
Questions people ask
How do you find the HCF using prime factors?
Write each number as a product of primes, then multiply the primes they share, using the smaller power each time. For 36 = 2^2 x 3^2 and 60 = 2^2 x 3 x 5, the shared part is 2^2 x 3 = 12.
What is the difference between a factor and a multiple?
A factor divides exactly into a number: the factors of 12 include 3 and 4. A multiple is in that number's times table: the multiples of 12 include 24 and 36. Factors are small or equal, multiples are big or equal.