How To Add Fractions Lcm

we want to determine the least commonmultiple, or lcm of eight and six. which would be the smallest number that's a multiple of both eight and six. and also the smallest number that can be divided evenly by eight and six. we'll show how to find the least common multiple using

How To Add Fractions Lcm, what's often called a fraction wall, aswell as how to find the least common multiple using loose rods. let's first use thefraction wall. so we'll define the smallest rod here asbeing equal to one whole. and therefore we also have a two rod, a three rod,

a four rod, a six rod, an eight rod, a twelve rod, and a twenty-four rod. to find the least common multiple of eight and six, we want to find the shortest train using eight rods, and six rods, where the twotrains would be exactly the same length. so looking at just the six rods here, and the eight rods here, we want to determine the shortest train in which the twotrains would be exactly the same length. so again, looking at the six rods here, and the eight rods here, notice how theshortest train

where the two trains would be the samelength, would be the train that starts here, and ends all the way over here, on the far right. so looking at just thesix rods now, notice how it would take one, two, three, four, six rods to form this train. so we have four copies of six, which means the length of this train would be twenty-four. notice how these four, six rods have the same length as one twenty-four rod. and now looking at the eight rods,

notice how it would take one, two, thee, eight rods to form the train of the same length. again this is the shortest train whereforming a train using six rods, and eight rods, would have the same length. so because we have three copies of eight, the length here is three times eight, of course the same length of twenty-four. which means the least common multiple of eight and six is twenty-four. twenty-four

is the smallest multiple of both eight and six. it's also the smallest number that isdivisible by both eight and six. now let's also show how we can build the lcm using loose rods. to find the least common multiple of eight and six, we'd begin with an eight rod, and a six rod. and now because the six rod is shorter we would add a six rod to form a six rod train, which would look like this. now noticehow the eight rod is shorter, so now we'd add an eight rod to form aneight rod train, which would look like this. notice howthe six rod

train is shorter, so we'd add another six rod to the six rod train, which would look like this. noticehow the trains are still not the same length. the eight rod train is shorter, so we addanother eight rod to the eight rod train. the trains are still not the same length.the six train is shorter, so we'd add another six rod to the six rodtrain. notice when we do this, finally the twotrains are the same length. this is the shortest train where we couldhave two trains of the same length using just six rods, and just eight rods.

notice how it takes three, eight rods, three times eight is twenty-four. and it takes four, six rods, four times six is also twenty-four. once again showing us that the leastcommon multiple of eight and six is twenty-four. i hope you found this illustration helpful.