Highest Common Factor and Lowest Common Multiple

The Highest Common Factor and Lowest Common Multiple of two numbers is found the same way; through prime factorisation.

The simplest way is prime factorisation trees. For them, you take the two numbers, say 150 and 95. Then, you for each number, you break it down into two factors – numbers that multiply to make it. For each number you get, you repeat the process, until you reach a prime number. Once you have only prime numbers, you take them out into two data sets for the next step.

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HCF

You then take the two data sets – one for the descendants of each original number – and compare them. You take out all the ones that are present in both and multiply them together, producing the HCF.

5,5,2,3
2,2,2,2,3

2 x 3 = 6
6 is the HCF of 150 and 96.

LCM

For LCM, you take the highest number of each number present in each set and multiply them all together.

5,5,2,3
2,2,2,2,3

5 x 5 x 2 x 2 x 2 x 2 x 3 = 1200
1200 is the LCM of 150 and 96.

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