Least Common Multiple (LCM) of 167 and 115
The least common multiple (LCM) of 167 and 115 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 167 and 115?
First, calculate the GCD of 167 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 115 = 1 remainder 52 |
| 2 | 115 ÷ 52 = 2 remainder 11 |
| 3 | 52 ÷ 11 = 4 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 176 | 12144 |
| 197 and 41 | 8077 |
| 183 and 131 | 23973 |
| 174 and 65 | 11310 |
| 18 and 27 | 54 |