Least Common Multiple (LCM) of 115 and 167
The least common multiple (LCM) of 115 and 167 is 19205.
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 167?
First, calculate the GCD of 115 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 167 = 0 remainder 115 |
| 2 | 167 ÷ 115 = 1 remainder 52 |
| 3 | 115 ÷ 52 = 2 remainder 11 |
| 4 | 52 ÷ 11 = 4 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 198 | 3762 |
| 13 and 63 | 819 |
| 144 and 186 | 4464 |
| 163 and 104 | 16952 |
| 195 and 165 | 2145 |