HCF And LCM

Question 1

What does HCF stand for?

Answer 1

Highest Common Factor

Question 2

What does LCM stand for?

Answer 2

Lowest Common Multiple

Question 3

What does Highest Common Factor mean?

Answer 3

It is the highest value that goes into two natural numbers.

Question 4

What is the Lowest Common Multiple?

Answer 4

It is the lowest possible result of two or more numbers that are multiplied together.

Question 5

How can you find the HCF and the LCM?

Answer 5

You can use prime factorisation.

Question 6

What is prime factorisation?

Answer 6

Prime factorisation is the process of finding a number as a product of its prime factors.

Question 7

How can we prime factorise numbers?

Answer 7

We can use the ladder method.

Question 8

How can the HCF be found using prime factorisation?

Answer 8

The HCF is found by multiplying the prime factors common to both numbers.
Prime factorise the numbers
Circle all prime factors in common
Multiply them together

Question 9

How can the LCM be found using prime factorisation?

Answer 9

The LCM is found by multiplying the highest exponential.
Prime factorise both numbers
Circle the highest power of each factor
Multiply them together

Question 10

Give an example of HCF by using 225 and 900.

Answer 10

For instance, the prime factorisation of 225 is 3x3x5x5. The prime factorisation of 900 is 2x2x3x3x5x5. They both have two 3s and two 5s. So to work out the HCF 3x3x5x5=225

Question 11

Give an example of LCM using 225 and 900.

Answer 11

For instance, the prime factorisation of 225 is 3squaredx5squared. The prime factorisation of 900 is 2squaredx3squaredx5squared. The highest exponent of 2 is squared. The highest exponent of 3 is squared. The highest exponent of 5 is squared. So to work out the LCM 2squaredx3squaredx5squared=900