Least Common Multiple (LCM) of 115 and 164
The least common multiple (LCM) of 115 and 164 is 18860.
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 115 and 164?
First, calculate the GCD of 115 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 164 = 0 remainder 115 |
| 2 | 164 ÷ 115 = 1 remainder 49 |
| 3 | 115 ÷ 49 = 2 remainder 17 |
| 4 | 49 ÷ 17 = 2 remainder 15 |
| 5 | 17 ÷ 15 = 1 remainder 2 |
| 6 | 15 ÷ 2 = 7 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 20 | 3180 |
| 158 and 139 | 21962 |
| 170 and 161 | 27370 |
| 63 and 142 | 8946 |
| 89 and 105 | 9345 |