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# Factors and Primes Problem Solving :/ watch

1. Hi, I was doing some IGCSE maths revision and I'm so stuck on one of the newer problem solving questions for factors and primes which is:
"n is a number. 100 is the LCM of 20 and n. Work out the two different possible values for n"
Does anyone know how to find the answer?
2. You're looking for factors of 100 that coincide with the multiples of 20 and another number. So just list all the factors of 100 if you're struggling and cross off the ones that are factors of 20 or where the least common multiple of that number and 20 is less than 100.
For example, 2 is a factor of 100 but lcm(2, 20)=20 so n cannot be 2.
5 is a factor of 100 but lcm(5, 20)=20 so n cannot be 5.
I'm not sure i've been able to make it as clear as I wanted to here.
3. 100, 50 and 25 would work. Just think of factors of 100 which are quite large so that there's unlikely to be any LCM's.
4. 100 is a multiple of n, therefore n * k = 100, where k is an integer. That can be written as n = 100 / k for an integer k. So a good place to start would be to divide 100 by 1 and see if that works, then divide it by 2, see if that works, divide it by 3, see if that works etc..
5. Multiple of 20= 20, 40, 60, 80, 100
Multiple of n = 100
N can be 25,50 because if 25
25,50,75,100
If 50
50,100
In both cases it's lcm is 100
If you see lcm is 100 here
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6. And to conclude 25 & 50 could be the values of N

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7. (Original post by Trevish)
And to conclude 25 & 50 could be the values of N

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or 100
8. Got it!
Thanks!

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