What Is the Lcm of 3 and 12?

The LCM of 3 and 12 is 12.

The least common multiple (LCM) of two integers is the smallest positive integer that is a multiple of both integers. LCM(3, 12) = 12.

The LCM is often used to find the lowest common denominator (LCD) of two or more fractions. The LCD is the smallest positive integer that is a multiple of all the denominators of the fractions. To find the LCD, we simply find the LCM of the denominators. For example, the LCD of 1/3, 1/4, and 1/6 is 12.

To find the LCM of 3 and 12, we list the multiples of each number:

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ... Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, ...

The smallest number that appears in both lists is 12, so 12 is the LCM of 3 and 12.

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In mathematics, the greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For example, the gcd of 8 and 12 is 4.

The greatest common divisor is also known as the greatest common factor (gcf), highest common factor (hcf), greatest common measure (gcm), or highest common divisor.

The greatest common divisor of two integers a and b is denoted as gcd(a,b).

A fresh viewpoint: Common Multiple

"What is the highest common factor of 3 and 12?"

The highest common factor of 3 and 12 is 3.

The highest common factor (HCF) of two or more numbers is the largest number that divides evenly into all of the numbers.

For example, the HCF of 24 and 30 is 6 because 6 divides evenly into 24 (4 times) and 30 (5 times).

To find the HCF of 3 and 12, we need to find the largest number that divides evenly into both 3 and 12.

The number 3 divides evenly into 3 and 12 (4 times and 4 times, respectively).

Therefore, the highest common factor of 3 and 12 is 3.

Broaden your view: What Is the Lcm of 4 and 10?

The smallest number that is a multiple of both 3 and 12 is 36. This is because 3 x 12 = 36, and 36 is the smallest possible number that satisfies this equation. There are other numbers that are also multiples of both 3 and 12 (such as 72, 108, 144, etc.), but 36 is the smallest number in this category.

Why is it important to find the smallest number that is a multiple of both 3 and 12? For many practical purposes, it is not particularly important. However, in some situations it can be helpful to know the smallest number in a given category. For example, if you are trying to find a number that is divisible by both 3 and 12, and you only want to consider numbers that are less than 100, then you would need to find the smallest number in this category, which is 36.

In general, finding the smallest number in a particular category can be helpful in many different situations. It can be used for optimization purposes, for example, or for finding the simplest solution to a problem. In some cases, it can also be used for educational purposes, as a way of helping people understand the concept of divisibility.

Curious to learn more? Check out: Roman Number

The largest number that is a multiple of both 3 and 12 is 36.

3 and 12 have a few things in common that make them fairly easy to work with when finding a common multiple. For one, they are both divisible by 3. This means that any number that is divisible by 3 is also divisible by 12. another thing that they have in common is that they are both even numbers. This means that any number that is divisible by 2 is also divisible by 12.

So, when looking for the largest number that is a multiple of both 3 and 12, we just need to find the smallest number that is divisible by 3 and 12. And that number is 36.

The smallest positive integer that is divisible by both 3 and 12 is 36. 36 is divisible by 3 because it is a multiple of 3, and it is divisible by 12 because it is a multiple of 12. 36 is the smallest positive integer that is divisible by both 3 and 12.

The largest positive integer that is divisible by both 3 and 12 is 36.

In mathematics, the least common multiple of two integers a and b, denoted by LCM(a, b), is the smallest positive integer that is evenly divisible by both a and b. For example, LCM(3, 12) = 12.

The least common multiple is useful in many applications. For example, it can be used to find the least common denominator of two or more fractions in order to add or compare them. It is also a key component in calculating the greatest common factor of two or more integers.

There are a few different ways to calculate the least common multiple of two integers. One way is to list the multiples of each integer until a common multiple is found. For example, the multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, and the multiples of 12 are 12, 24, 36. The least common multiple of 3 and 12 is therefore 12.

Another way to calculate the least common multiple is to use the greatest common factor (GCF). The greatest common factor of two integers is the largest integer that evenly divides both integers. The greatest common factor of 3 and 12 is 3. Therefore, the least common multiple of 3 and 12 is 3 x 12 = 36.

There are a few other methods of calculating the least common multiple, but these are the two most common methods. In general, the least common multiple of two or more integers is the smallest positive integer that is evenly divisible by all of the integers.

The greatest common factor (GCF) of two or more whole numbers is the largest whole number that divides evenly into each of the numbers. The GCF of 3 and 12 is 3.

For more insights, see: What Is 3 1/2 as a Whole Number?