Please carry out numbers be separate by a comma "," and also click the "Calculate" switch to uncover the LCM.

You are watching: What is the least common multiple of 12 and 7?

 330, 75, 450, 225

RelatedGCF hunterriverpei.com | element hunterriverpei.com

### What is the Least typical Multiple (LCM)?

In mathematics, the least usual multiple, also known together the lowest common multiple of two (or more) integers a and b, is the smallest optimistic integer the is divisible through both. That is typically denoted as LCM(a, b).

### Brute force Method

There room multiple means to uncover a least common multiple. The most straightforward is simply using a "brute force" method that lists out each integer"s multiples.

 EX: Find LCM(18, 26)18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 23426: 52, 78, 104, 130, 156, 182, 208, 234

As can be seen, this an approach can be reasonably tedious, and also is far from ideal.

See more: How Was The Estates-General Useful In Uniting France Under One National Identity?

### Prime factorization Method

A more systematic means to discover the LCM that some provided integers is to use prime factorization. Prime factorization requires breaking down each of the number being compared into that product of element numbers. The LCM is then established by multiplying the highest possible power of every prime number together. Note that computing the LCM this way, while an ext efficient than using the "brute force" method, is still limited to smaller numbers. Refer to the example below for clear up on exactly how to usage prime factorization to determine the LCM:

 EX: Find LCM(21, 14, 38)21 = 3 × 714 = 2 × 738 = 2 × 19The LCM is therefore:3 × 7 × 2 × 19 = 798

### Greatest usual Divisor Method

A third viable technique for finding the LCM the some provided integers is making use of the greatest usual divisor. This is additionally frequently referred to as the greatest common factor (GCF), amongst other names. Refer to the connect for details on just how to determine the greatest typical divisor. Given LCM(a, b), the procedure for finding the LCM utilizing GCF is to divide the product that the numbers a and b by your GCF, i.e. (a × b)/GCF(a,b). Once trying to identify the LCM of more than 2 numbers, for instance LCM(a, b, c) find the LCM the a and b whereby the an outcome will be q. Then discover the LCM of c and q. The an outcome will it is in the LCM the all 3 numbers. Making use of the vault example:

 EX: Find LCM(21, 14, 38)GCF(14, 38) = 2LCM(14, 38) = 38 × 14 2
= 266GCF(266, 21) = 7
 LCM(266, 21) = 266 × 21 7
= 798LCM(21, 14, 38) = 798

Note that it is not necessary which LCM is calculated very first as lengthy as every the numbers space used, and also the method is followed accurately. Relying on the details situation, each an approach has its very own merits, and also the user have the right to decide which technique to pursue at their very own discretion.