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 |
|---|---|
| 122 and 83 | 10126 |
| 67 and 65 | 4355 |
| 96 and 117 | 3744 |
| 174 and 200 | 17400 |
| 24 and 186 | 744 |