- Prime Numbers Factors and Multiples
- Home
- Even and Odd Numbers
- Divisibility Rules for 2, 5, and 10
- Divisibility Rules for 3 and 9
- Factors
- Prime Numbers
- Prime Factorization
- Greatest Common Factor of 2 Numbers
- Greatest Common Factor of 3 Numbers
- Introduction to Distributive Property
- Understanding the Distributive Property
- Introduction to Factoring With Numbers
- Factoring a Sum or Difference of Whole Numbers
- Least Common Multiple of 2 Numbers
- Least Common Multiple of 3 Numbers
- Word Problem Involving the Least Common Multiple of 2 Numbers

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
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# Least Common Multiple of 2 Numbers

The **multiple** of a number is that number multiplied by an integer. The multiples of a number are found by multiplying it with 1, 2, 3, 4....and so on.

For **example**, the multiples of 4 are 4 × 1, 4 × 2, 4 × 3, 4 × 4,...or 4, 8, 12, 16 ...and so on.

The multiples of two numbers that are common to both the numbers are known as **common multiples** of those numbers.

The smallest positive number that is a common multiple of two numbers is the **least common multiple or (lcm)** of those two numbers.

The **least common mulitple** of two numbers is also the smallest number that both the numbers divide completely without leaving a remainder.

**Rules to find the least common multiple of two numbers**

- We begin by listing the first few multiples of the two numbers.
- Then we look for the common multiples of both the numbers.
- The first common multiple of the numbers would be their least common multiple.

Find the least common multiple of 8 and 10

### Solution

**Step 1:**

The multiples of 8 and 10 are as follows

Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, **80**...

Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, **80**...

**Step 2:**

The first common multiple of 8 and 10 is 80, which is their least common multiple (lcm)

Find the least common multiple of 12 and 18

### Solution

**Step 1:**

The multiples of 12 and 18 are as follows

Multiples of 12 = 12, 24, **36** , 48, 60, **72**, 84...

Multiples of 18 = 18, **36**, 54, **72**, 90, 108...

**Step 2:**

The first common multiple of 12 and 18 is 36, which is their least common multiple (lcm)

Find the least common multiple of 9 and 15

### Solution

**Step 1:**

The multiples of 9 and 15 are as follows

Multiples of 9 = 9, 18, 27, 36, **45**, 54...

Multiples of 15 = 15, 30, **45**, 60...

**Step 2:**

The first common multiple of 9 and 15 is 45, which is their least common multiple (lcm)