Least Common Multiple (LCM) of 193 and 167
The least common multiple (LCM) of 193 and 167 is 32231.
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 193 and 167?
First, calculate the GCD of 193 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 167 = 1 remainder 26 |
| 2 | 167 ÷ 26 = 6 remainder 11 |
| 3 | 26 ÷ 11 = 2 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 108 | 3132 |
| 100 and 164 | 4100 |
| 34 and 75 | 2550 |
| 48 and 169 | 8112 |
| 91 and 109 | 9919 |