Least Common Multiple (LCM) of 135 and 187
The least common multiple (LCM) of 135 and 187 is 25245.
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 187?
First, calculate the GCD of 135 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 187 = 0 remainder 135 |
| 2 | 187 ÷ 135 = 1 remainder 52 |
| 3 | 135 ÷ 52 = 2 remainder 31 |
| 4 | 52 ÷ 31 = 1 remainder 21 |
| 5 | 31 ÷ 21 = 1 remainder 10 |
| 6 | 21 ÷ 10 = 2 remainder 1 |
| 7 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 84 | 3780 |
| 122 and 189 | 23058 |
| 60 and 18 | 180 |
| 170 and 85 | 170 |
| 168 and 184 | 3864 |