Least Common Multiple (LCM) of 167 and 135
The least common multiple (LCM) of 167 and 135 is 22545.
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 135?
First, calculate the GCD of 167 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 135 = 1 remainder 32 |
| 2 | 135 ÷ 32 = 4 remainder 7 |
| 3 | 32 ÷ 7 = 4 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 112 | 7504 |
| 138 and 24 | 552 |
| 180 and 82 | 7380 |
| 126 and 65 | 8190 |
| 76 and 87 | 6612 |