Least common multiple (video) | Khan Academy
Thus, 9 x LCM = LCM = / 9 LCM = For any more questions of such type you can visit Relationship b For any more questions of such type you can visit Relationship between H.C.F. and L.C.M. . = 2* 3*3 * If the HCF of 2 numbers is 13 and their product is , then what is their LCM?. The lowest common multiple of two integers a and b is the smallest integer than is multiple of these Method 3: use the GCD value and use the formula LCM(a, b ) = a * b / GCD(a, b) LCM(1,2,3 9,10)=, LCM(1,2,3 12,13)=, Common multiples are multiples that two numbers have in common. These can be useful Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27 Common multiples of 2 .
It's 1 times So the smallest number that is both a multiple of 36 and because 36 is a multiple of is actually Let's do a couple more of these.
- LCM (Lowest Common Multiple)
- Least common multiple
That one was too easy. What is the least common multiple of 18 and 12?
Multiples, Factors and Powers
And they just state this with a different notation. The least common multiple of 18 and 12 is equal to question mark. So let's think about this a little bit.
So there's a couple of ways you can think about-- so let's just write down our numbers that we care about. We care about 18, and we care about So there's two ways that we could approach this. One is the prime factorization approach. We can take the prime factorization of both of these numbers and then construct the smallest number whose prime factorization has all of the ingredients of both of these numbers, and that will be the least common multiple.
So let's do that.
Number opposites (video) | Negative numbers | Khan Academy
So we could write 18 is equal to 2 times 3 times 3. That's its prime factorization. So 12 is equal to 2 times 2 times 3. Now, the least common multiple of 18 and let me write this down-- so the least common multiple of 18 and 12 is going to have to have enough prime factors to cover both of these numbers and no more, because we want the least common multiple or the smallest common multiple. So let's think about it. Well, it needs to have at least 1, 2, a 3 and a 3 in order to be divisible by So let's write that down.
So we have to have a 2 times 3 times 3.
This makes it divisible by If you multiply this out, you actually get And now let's look at the So this part right over here-- let me make it clear. This part right over here is the part that makes up 18, makes it divisible by Hence write down the LCM of 12, 16 and 24? Solution a The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96,,… The multiples of 16 are 16, 32, 48, 64, 80, 96,,… Hence the common multiples of 12 and 16 are 48, 96, ,… and their LCM is Two or more nonzero numbers always have a common multiple — just multiply the numbers together.
But the product of the numbers is not necessarily their lowest common multiple. What is the general situation illustrated here?
Solution The LCM of 9 and 10 is their product The common multiples are the multiples of the LCM You will have noticed that the list of common multiples of 4 and 6 is actually a list of multiples of their LCM Similarly, the list of common multiples of 12 and 16 is a list of the multiples of their LCM This is a general result, which in Year 7 is best demonstrated by examples.
In an exercise at the end of the module, Primes and Prime Factorisationhowever, we have indicated how to prove the result using prime factorisation. This can be restated in terms of the multiples of the previous section: On the other hand, zero is the only multiple of zero, so zero is a factor of no numbers except zero.
These rather odd remarks are better left unsaid, unless students insist. They should certainly not become a distraction from the nonzero whole numbers that we want to discuss. The product of two nonzero whole numbers is always greater than or equal to each factor in the product.