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April 11th, 2015, 11:40 AM  #1 
Newbie Joined: Apr 2015 From: United Kingdom Posts: 1 Thanks: 0  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: 
April 11th, 2015, 12:05 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,622 Thanks: 2074 
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?

April 11th, 2015, 01:42 PM  #3 
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 390 Thanks: 70 
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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