Least Common Multiple (LCM) of 135 and 186
The least common multiple (LCM) of 135 and 186 is 8370.
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 186?
First, calculate the GCD of 135 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 186 = 0 remainder 135 |
| 2 | 186 ÷ 135 = 1 remainder 51 |
| 3 | 135 ÷ 51 = 2 remainder 33 |
| 4 | 51 ÷ 33 = 1 remainder 18 |
| 5 | 33 ÷ 18 = 1 remainder 15 |
| 6 | 18 ÷ 15 = 1 remainder 3 |
| 7 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 82 | 5658 |
| 194 and 185 | 35890 |
| 186 and 110 | 10230 |
| 102 and 141 | 4794 |
| 155 and 100 | 3100 |