Log in Cameron Christensen 11 years agoPosted 11 years ago. Direct link to Cameron Christensen's post “Is the LCM (Least Common ...” Is the LCM (Least Common Multiple) useful in real life? If so, could someone provide some examples? • (244 votes) Michael Wais Jr 11 years agoPosted 11 years ago. Direct link to Michael Wais Jr's post “I'm assuming that if you'...” I'm assuming that if you're baking something, like a really extravagant cake or something, then figuring out the least common multiple just might work when you're trying to figure out how many cartons of eggs to get to satisfy the ingredients. Also, it might work when trying to figure out if a discount is worth it when you're at the supermarket and comparing any of the "2 for $2" or "5 for $5" types of deals. It's almost (29 votes) Tyler 11 years agoPosted 11 years ago. Direct link to Tyler's post “is the least common facto...” is the least common factor the same as the lcm? • (38 votes) Christi 11 years agoPosted 11 years ago. Direct link to Christi's post “No. LCM stands for Least...” No. LCM stands for Least Common Multiple. A multiple is a number you get when you multiply a number by a whole number (greater than 0). A factor is one of the numbers that multiplies by a whole number to get that number. example: the multiples of 8 are 8, 16, 24, 32, 40, 48, 56... The term least common factor doesn't really make sense since the least common factor of any pair of numbers is 1. Not exactly a useful piece of knowledge. (123 votes) Jae 10 years agoPosted 10 years ago. Direct link to Jae's post “finding the LCM is too ha...” finding the LCM is too hard for me! Can anyone give me advice for remembering? • (18 votes) Anthony Jacquez 10 years agoPosted 10 years ago. Direct link to Anthony Jacquez's post “All you have to do is lis...” All you have to do is list the multiplies of both of the numbers and look for the common number. Example: Example: Example: (68 votes) Cassandra Martin 8 years agoPosted 8 years ago. Direct link to Cassandra Martin's post “what if the number you ha...” what if the number you have has no multiples? • (13 votes) Noureen Aneeze 7 years agoPosted 7 years ago. Direct link to Noureen Aneeze's post “There is no number withou...” There is no number without multiples and factors. For factors, there will always be 1 and itself. For multiples, take any number and multiply it with your number. Hope this helps! (19 votes) justvicky :3 4 years agoPosted 4 years ago. Direct link to justvicky :3's post “Can we use other methods ...” Can we use other methods to find LCM? • (10 votes) Ian Pulizzotto 4 years agoPosted 4 years ago. Direct link to Ian Pulizzotto's post “Good question!There is ...” Good question! There is a prime factorization method for finding the LCM of a list of two or more numbers. Prime-factor each number. Then for each prime factor, use the greatest number of times it appears in any prime factorization. Example: Find the LCM of 40, 48, and 72. The prime factor 2 occurs a maximum of four times, the prime factor 3 occurs a maximum of two times, and the prime factor 5 occurs a maximum of one time. No other prime factors appear at all. So the LCM is 2*2*2*2*3*3*5 = 720. By the way, there is a similar method of finding GCF (or HCF or GCD or HCD, where G means greatest, H means highest, F means factor, and D means divisor), but we use each prime factor the least number of times it appears in any prime factorization. In our example, the GCF would be 2*2*2 = 8. An interesting property of GCF and LCM is that, for two numbers, the product of the numbers always equals the GCF times the LCM. However, this might not be true for three or more numbers. (20 votes) TheOGTristan 5 years agoPosted 5 years ago. Direct link to TheOGTristan's post “Can the Least common mult...” Can the Least common multiple also be the greatest common multiple • (10 votes) MITSKIIII 3 years agoPosted 3 years ago. Direct link to MITSKIIII's post “Well yes, in a way. For ...” Well yes, in a way. For 0 the only multiple is 0, and nothing else. There's been confusion about 1 having no multiples. But, all the whole numbers are multiples of 1. (3 votes) julia 7 years agoPosted 7 years ago. Direct link to julia's post “what is the difference be...” what is the difference between multiple and factor? • (9 votes) Goldleaf 7 years agoPosted 7 years ago. Direct link to Goldleaf's post “They both involve multipl...” They both involve multiplication. Factors are what you multiply to get a number. Multiples are what we get after multiplying the number by an integer (number, not a fraction). Example: 2 x 2 are factors and 4 is the multiple. (3 votes) katrina 10 years agoPosted 10 years ago. Direct link to katrina's post “what is the difference be...” what is the difference between a multiple and a factor? • (4 votes) Karen Copstead 10 years agoPosted 10 years ago. Direct link to Karen Copstead's post “Multiples and factors are...” Multiples and factors are both about multiplying, as follows.. (11 votes) Kiba 4 years agoPosted 4 years ago. Direct link to Kiba's post “Hello, why is it that whe...” Hello, why is it that when he factorizes, he only gets picks 1 number from the 12? And why that specific number? • (5 votes) Hecretary Bird 4 years agoPosted 4 years ago. Direct link to Hecretary Bird's post “You can really only divid...” You can really only divide 12 by one number at a time. The order that you do it doesn't really matter. In the video, Sal went from 12 to 2 and 6, but you could just as easily go from 12 to 3 and 4. Decompose the 4 into 2 * 2 and you get the same result as he did. (9 votes) Monish Sarkar 6 years agoPosted 6 years ago. Direct link to Monish Sarkar's post “But can't all the numbers...” But can't all the numbers be broken down by 1? • (4 votes) kubleeka 6 years agoPosted 6 years ago. Direct link to kubleeka's post “Yes, but that doesn't act...” Yes, but that doesn't actually leave us with different numbers, so we ignore divisibility by 1. (3 votes)Want to join the conversation?
10:30
the factors of 8 are 1, 2, 4, 8.
5 and 6
5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
The LMC of 5 and 6 is 30.
10 and 12
10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
The LMC of 10 and 12 is 60.
3 and 7
3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70
The LMC of 3 and 7 is 21.
eg: factor of a number d = 1 and d
If the number is 1, then the factor is 1.
eg: multiple of a number y = y * another number x
40 = 2*2*2*5
48 = 2*2*2*2*3
72 = 2*2*2*3*3
A multiple is what you get when you multiply a number by other numbers, like, we get 10, 15, 20, 25, 30 and on and on, which are some MULTIPLES of 5, for example.
(A multiple, is bigger than the number.)
A FACTOR, is what you can multiply together to get a number. Like the factors of 24, can be 1, 2, 3, 4, 6, 8, and 12. These are FACTORS of 24, for example, because you can multiply 2 times 12 to get 24. (The factors of a certain number are smaller than the number.
Video transcript
What is the least commonmultiple of 36 and 12? So another way to say this isLCM, in parentheses, 36 to 12. And this is literallysaying what's the least commonmultiple of 36 and 12? Well, this one mightpop out at you, because 36 itselfis a multiple of 12. And 36 is also a multiple of 36. It's 1 times 36. So the smallest number that isboth a multiple of 36 and 12-- because 36 is a multipleof 12-- is actually 36. There we go. Let's do a couple more of these. That one was too easy. What is the least commonmultiple of 18 and 12? And they just state thiswith a different notation. The least commonmultiple of 18 and 12 is equal to question mark. So let's think aboutthis a little bit. So there's a couple of waysyou can think about-- so let's just write down ournumbers that we care about. We care about 18,and we care about 12. So there's two ways thatwe could approach this. One is the primefactorization approach. We can take the primefactorization of both of these numbersand then construct the smallest numberwhose prime factorization has all of the ingredientsof both of these numbers, and that will be theleast common multiple. So let's do that. 18 is 2 times 9, which isthe same thing as 2 times 3 times 3, or 18 is 2 times 9. 9 is 3 times 3. So we could write 18 isequal to 2 times 3 times 3. That's its prime factorization. 12 is 2 times 6. 6 is 2 times 3. So 12 is equal to2 times 2 times 3. Now, the least commonmultiple of 18 and 12-- let me write this down-- sothe least common multiple of 18 and 12 is going to have to haveenough prime factors to cover both of thesenumbers and no more, because we want the leastcommon multiple or the smallest common multiple. So let's think about it. Well, it needs to have atleast 1, 2, a 3 and a 3 in order to be divisible by 18. So let's write that down. So we have to havea 2 times 3 times 3. This makes it divisible by 18. If you multiply thisout, you actually get 18. And now let's look at the 12. So this part right overhere-- let me make it clear. This part right overhere is the part that makes up 18, makesit divisible by 18. And then let's see. 12, we need two 2's and a 3. Well, we already have one 3,so our 3 is taken care of. We have one 2, so this2 is taken care of. But we don't have two 2s's. So we need another 2 here. So, notice, now this numberright over here has a 2 times 2 times 3 in it, or it has a12 in it, and it has a 2 times 3 times 3, or an 18 in it. So this right over here isthe least common multiple of 18 and 12. If we multiply it out,so 2 times 2 is 4. 4 times 3 is 12. 12 times 3 is equal to 36. And we are done. Now, the other wayyou could've done it is what I would sayjust the brute force method of just looking at themultiples of these numbers. You would say, well, let's see. The multiples of 18are 18, 36, and I could keep goinghigher and higher, 54. And I could keep going. And the multiples of12 are 12, 24, 36. And immediately I say, well, Idon't have to go any further. I already found amultiple of both, and this is the smallestmultiple of both. It is 36. You might say, hey,why would I ever do this one right over hereas opposed to this one? A couple of reasons. This one, you'rekind of-- it's fun, because you're actuallydecomposing the number and then building it back up. And also, this is a betterway, especially if you're doing it with really, reallylarge and hairy numbers. Really, really, reallylarge and hairy numbers where you keep trying tofind all the multiples, you might have to go prettyfar to actually figure out what their leastcommon multiple is. Here, you'll be able to do it alittle bit more systematically, and you'll knowwhat you're doing.
