Least Common Multiple (LCM) of 113 and 162
The least common multiple (LCM) of 113 and 162 is 18306.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 113 and 162?
First, calculate the GCD of 113 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 162 = 0 remainder 113 |
| 2 | 162 ÷ 113 = 1 remainder 49 |
| 3 | 113 ÷ 49 = 2 remainder 15 |
| 4 | 49 ÷ 15 = 3 remainder 4 |
| 5 | 15 ÷ 4 = 3 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 96 | 8544 |
| 102 and 135 | 4590 |
| 114 and 128 | 7296 |
| 110 and 189 | 20790 |
| 112 and 94 | 5264 |