We want to find three numbers that have a least common multiple of 100. To do so, recall that a factor pair is a combination of two factors that can be multiplied together to equal a number. Let's find the factor pairs of 100 by listing its factors!
Factors of100: 1,2,4,5,10,20,25,50,100
Now, we can write the factor pairs of each number by finding the product of two factors that equals 100.
Remember that when a number is multiplied by an integer, the result is a multiple of the first number.
Note that the above products have the same form as the products we used to find the factor pairs. Then, we can list these products to identify the numbers that have 100 as a multiple. Let's do it!
1 * 100 &= 100 → 100 is multiple of 1
100 * 1 &= 100 → 100 is multiple of 100
2 * 50 &= 100 → 100 is multiple of 2
50 * 2 &= 100 → 100 is multiple of 50
4 * 25 &= 100 → 100 is multiple of 4
25 * 4 &= 100 → 100 is multiple of 25
5 * 20 &= 100 → 100 is multiple of 5
20 * 5 &= 100 → 100 is multiple of 20
10 * 10 &= 100 → 100 is multiple of 10
Now we can list the multiples of the numbers that have 100 as a factor to find three numbers with an LCM equal to 100. Let's ignore the 1 and 100 because they are the identities.
Multiples of2&: 2,4,6,8,10,12,14,16,18,20,...
Multiples of4&: 4,8,12,16,20,24,28,32,36,...
Multiples of5&: 5,10,15,...,95, 100,105,110,...
Multiples of10&: 10,20,30,...,70,80,90,100,...
Multiples of20&: 20,40,60,80, 100,120,140,...
Multiples of25&: 25,50,75, 100,125,150,175,...
Multiples of50&: 50, 100,150,200,250,300,350,...
From the above list, we can see that 5, 20, and 25 have an LCM of 100. Note that there are other three-number sets we could create out of this list that have an LCM of 100.
