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 |
|---|---|
| 153 and 199 | 30447 |
| 101 and 45 | 4545 |
| 80 and 75 | 1200 |
| 192 and 146 | 14016 |
| 130 and 159 | 20670 |