GCSE Edexcel Maths Probability: 1. (a) Write 84 as a product of

1. (a) Write 84 as a product of its prime factors - Edexcel - GCSE Maths - Question 2 - 2020 - Paper 2

Question 2

1. (a) Write 84 as a product of its prime factors. (b) Find the lowest common multiple (LCM) of 60 and 84.

Worked Solution & Example Answer:1. (a) Write 84 as a product of its prime factors - Edexcel - GCSE Maths - Question 2 - 2020 - Paper 2

Step 1

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Answer

To express 84 as a product of its prime factors, we can use a factor tree approach:

Start by dividing 84 by the smallest prime number, which is 2: $84 \div 2 = 42$
Next, divide 42 by 2: $42 \div 2 = 21$
Now, divide 21 by the smallest prime number that can divide it, which is 3: $21 \div 3 = 7$
Lastly, since 7 is a prime number, we stop here.

Putting this all together, we get: $84 = 2^2 \times 3^1 \times 7^1$

Step 2

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Answer

To find the LCM of 60 and 84, we first need to express both numbers as products of their prime factors:

Next, we take the highest power of each prime factor involved:

Now we multiply these together to find the LCM: $LCM = 2^2 \times 3^1 \times 5^1 \times 7^1 = 420$