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2 (a) Write down (i) a multiple of 13, (ii) a prime number between 40 and 50 - OCR - GCSE Maths - Question 2 - 2017 - Paper 1

Question 2

2 (a) Write down (i) a multiple of 13, (ii) a prime number between 40 and 50. (b) Find the lowest common multiple (LCM) of 16 and 28.

Worked Solution & Example Answer:2 (a) Write down (i) a multiple of 13, (ii) a prime number between 40 and 50 - OCR - GCSE Maths - Question 2 - 2017 - Paper 1

Step 1

a(i) a multiple of 13

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Answer

A multiple of 13 is obtained by multiplying 13 by any integer. For example, taking 13 times 1 gives us 13, and taking 13 times 2 gives us 26. Therefore, any multiple such as 13, 26, 39, 52, etc., can be considered valid answers. Here, we can choose 26 as a valid multiple.

Step 2

a(ii) a prime number between 40 and 50

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Answer

The prime numbers between 40 and 50 are 41, 43, 47. Among these, any of the three can be chosen as a valid answer. Here, we can select 41.

Step 3

b) Find the lowest common multiple (LCM) of 16 and 28

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Answer

To find the least common multiple (LCM) of 16 and 28, we first find the prime factorization of each number:

16: $2^4$
28: $2^2 \times 7^1$

The LCM is found by taking the highest power of each prime factor:

From $2$ : the highest power is $2^4$
From $7$ : the highest power is $7^1$

Thus, the LCM is:

$LCM = 2^4 \times 7^1 = 16 \times 7 = 112$

Therefore, the LCM of 16 and 28 is 112.

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