Question

(Smallest common multiple of 54 and 45) X (Biggest common factor of 20 points
and 35) is equal to-
*​

Answer 1

Answer:

The highest common factor (HCF) of two whole numbers

is the largest whole number which is a factor of both.

HCF Example

Consider the numbers 12 and 15:

The factors of 12 are : 1, 2, 3, 4, 6, 12.

The factors of 15 are : 1, 3, 5, 15.

1 and 3 are the only common factors (numbers which are factors of both 12 and 15).

Therefore, the highest common factor of 12 and 15 is 3.

Example Questions

Work out the answers to these questions and click the buttons marked Click on this button below to see the correct answer to see whether you are correct.

(a) Find the highest common factor of 20 and 30 by following the steps below:

What are the factors of 20?

What are the factors of 30?

What is the highest common factor of 20 and 30?

(b) Find the highest common factor of 14 and 12 by following the steps below:

What are the factors of 14?

What are the factors of 12?

What is the highest common factor of 14 and 12?

The lowest common multiple (LCM) of two whole numbers

is the smallest whole number which is a multiple of both.

LCM Example

Consider the numbers 12 and 15 again:

The multiples of 12 are : 12, 24, 36, 48, 60, 72, 84, ....

The multiples of 15 are : 15, 30, 45, 60, 75, 90, ....

60 is a common multiple (a multiple of both 12 and 15), and there are no lower common multiples.

Therefore, the lowest common multiple of 12 and 15 is 60.

Example Questions

Work out the answers to these questions and click the buttons marked Click on this button below to see the correct answer to see whether you are correct.

(a) Find the lowest common multiple of 5 and 7 by following the steps below:

What are the first ten multiples of 5?

What are the first ten multiples of 7?

What is the lowest common multiple of 5 and 7?

(b) Find the lowest common multiple of 6 and 10 by following the steps below:

What are the first ten multiples of 6?

What are the first ten multiples of 10?

What is the lowest common multiple of 6 and 10?

Although the methods above work well for small numbers, they are

more difficult to follow with bigger numbers. Another way to find the

highest common factor and lowest common multiple of a pair of

numbers is to use the prime factorisations of the two numbers.