The (LCM) of two numbers is the smallest whole number that is a of both numbers. Let's see a few examples!
Numbers
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Multiples of Numbers
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Common Multiples
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Least Common Multiple
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2 and 3
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Multiples of 2:Multiples of 3: 2,4,6,8,10,12,… 3,6,9,12,15,…
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6,12,18,24,…
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LCM(2,3)=6
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8 and 12
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Multiples of 8:Multiples of 12: 8,16,24,32,40,48,… 12,24,36,48,…
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24,48,72,96,…
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LCM(8,12)=24
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We want to find three numbers that have a least common multiple of
100. To do so, recall that a is a combination of two that can be multiplied together to equal a number. Let's find the factor pairs of
100 by listing its factors!
Factors of 100:1,2,4,5,10,20,25,50,100
Now, we can write the factor pairs of each number by finding the product of two factors that equals
100.
Number
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Product of Two Factors
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Factor Pairs
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100
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1×100=10002×50=10004×25=10005×20=10010×10=100
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(1,100)(2,50)(4,25)(5,20)(10,10)
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Remember that when a number is multiplied by an , 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!
1×100100×12×5050×24×2525×45×2020×510×10=100 → 100 is multiple of 1=100 → 100 is multiple of 100=100 → 100 is multiple of 2=100 → 100 is multiple of 50=100 → 100 is multiple of 4=100 → 100 is multiple of 25=100 → 100 is multiple of 5=100 → 100 is multiple of 20=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 of 2Multiples of 4Multiples of 5Multiples of 10Multiples of 20Multiples of 25Multiples of 50:2,4,6,8,10,12,14,16,18,20,...:4,8,12,16,20,24,28,32,36,...:5,10,15,...,95,100,105,110,...:10,20,30,...,70,80,90,100,...:20,40,60,80,100,120,140,...:25,50,75,100,125,150,175,...: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.