HCF and LCM exam questions

Understanding HCF and LCM

HCF stands for Highest Common Factor, which is the largest number that divides exactly into two or more given numbers.
LCM denotes Lowest Common Multiple, referring to the smallest number that is a multiple of two or more given numbers.
These concepts are fundamental in number theory and have applications in solving problems related to ratios, fractions, and divisibility.

To find the HCF of two numbers, list all the factors of each number. The HCF is the highest number that appears in both lists.
The LCM can be found by listing multiples of the numbers until you find a common value - this is your LCM. Alternatively, use the formula: LCM(a, b) = (a*b) / HCF(a,b).

The HCF is used when reducing fractions to their simplest form. The HCF of the numerator and denominator is used to divide both, giving the simplest form.
The LCM is often used when adding or subtracting fractions with different denominators. The LCM of the denominators is used as the common denominator to make the calculation simpler.

Word problems often use HCF and LCM in context, such as organising events, scheduling, or planning. Recognising these types of problems and applying HCF and LCM correctly is key to finding solutions.

Mixing up the definitions of HCF and LCM. Always remember: HCF is the highest number that divides into the numbers, and the LCM is the smallest number that the numbers divide into.
Overlooking factors or multiples when listing them out, resulting in an incorrect HCF or LCM.
Forgetting to reduce fractions to their simplest form using the HCF.
Not using the LCM as the common denominator when adding or subtracting fractions with different denominators.