Least Common Multiple (LCM) of 167 and 129
The least common multiple (LCM) of 167 and 129 is 21543.
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 129?
First, calculate the GCD of 167 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 129 = 1 remainder 38 |
| 2 | 129 ÷ 38 = 3 remainder 15 |
| 3 | 38 ÷ 15 = 2 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 10 | 270 |
| 36 and 108 | 108 |
| 135 and 33 | 1485 |
| 37 and 34 | 1258 |
| 86 and 152 | 6536 |