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April 11th, 2015, 11:40 AM   #1
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Tricky HCM and LCF question:

Hi, I got really stuck with this question and I would really appreciate some help on how to work it out:

Martin thinks of 2 numbers. He says the HCF of the 2 numbers is 6 and the LCM is a multiple of 15. Write down the 2 possible numbers that Martin is thinking of:
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April 11th, 2015, 12:05 PM   #2
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Each number is divisible by 6 and just one of the numbers is divisible by 5, so the numbers are 6m and 30n, where m and n are any natural numbers whose HCF is 1. Do you now understand why?
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April 11th, 2015, 01:42 PM   #3
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An algorithmic techique:

Choose the HCF for the first number.
To get the second number, factor the HCF and the LCM

6=2×3
15=3×5
Put a stroke through the common factors, in this case the two 3s.
Now write out the factors as a product, counting the 3s just once:
2×3×5=30
The second number is 30.

Another example: Find two numbers such that the HCF is 20 and the LCM is 30.
Answer: The first number is 20.
20 = 2×2×5
30 = 2×3×5
The second number is 2×2×3×5, that is 60.
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