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Cambridge O Level Mathematics Vol. 1 7. Write down a list of numbers between 80 and 90, including 80 and 90. From your list find: (a) two prime numbers, (b) three multiples of 5, (c) a factor of 348.
Highest Common Factor (HCF) and Lowest Common Multiple (LCM) Common means ‘belonging to all’. We often need to find the factors or multiples of two (or more) numbers that belong to both (or all) the numbers. One way to do this is to list all the factors or multiples of both numbers and see which factors or multiples occur in both lists. The following example shows how this is done. Example 5 (a) (i) List all the factors of 30. (ii) List all the factors of 20. (iii) From your two lists find the common factors of 20 and 30 (not including 1). (b) (i) List the first four multiples of 30 (not including 30 itself ). (ii) List the first five multiples of 20 (not including 20 itself ). (iii) From your two lists, find any common multiples. (c) Find the HCF of 30 and 20. (d) Find the LCM of 30 and 20. Answer 5 (a) (i) {1, 2, 3, 5, 6, 10, 15, 30} (ii) {1, 2, 4, 5, 10, 20} (iii) {2, 5, 10} (c) 10
(b) (i) {60, 90, 120, 150} (ii) {40, 60, 80, 100, 120} (iii) {60, 120} (d) 60
Using the above example you should see that finding the highest common factor (HCF) of 20 and 30 is simple. It is the highest number that appears in both lists of factors of both the numbers. The HCF of 20 and 30 is 10. Similarly, the lowest common multiple of 20 and 30 is the smallest number that appears in both lists of multiples. The LCM of 20 and 30 is 60.
Tests of Divisibility without using a Calculator Before you go any further you might like to try some tests of divisibility which can help you save time in these questions. These tests show what will divide into a number without leaving a remainder.
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