Least Common Multiple (LCM) of 186 and 135
The least common multiple (LCM) of 186 and 135 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 186 and 135?
First, calculate the GCD of 186 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 135 = 1 remainder 51 |
| 2 | 135 ÷ 51 = 2 remainder 33 |
| 3 | 51 ÷ 33 = 1 remainder 18 |
| 4 | 33 ÷ 18 = 1 remainder 15 |
| 5 | 18 ÷ 15 = 1 remainder 3 |
| 6 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 77 | 1540 |
| 134 and 116 | 7772 |
| 63 and 91 | 819 |
| 159 and 33 | 1749 |
| 58 and 64 | 1856 |