Least Common Multiple (LCM) of 135 and 167
The least common multiple (LCM) of 135 and 167 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 135 and 167?
First, calculate the GCD of 135 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 167 = 0 remainder 135 |
| 2 | 167 ÷ 135 = 1 remainder 32 |
| 3 | 135 ÷ 32 = 4 remainder 7 |
| 4 | 32 ÷ 7 = 4 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 53 | 6307 |
| 178 and 77 | 13706 |
| 68 and 10 | 340 |
| 138 and 82 | 5658 |
| 99 and 180 | 1980 |