Least Common Multiple (LCM) of 137 and 189
The least common multiple (LCM) of 137 and 189 is 25893.
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 137 and 189?
First, calculate the GCD of 137 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 189 = 0 remainder 137 |
| 2 | 189 ÷ 137 = 1 remainder 52 |
| 3 | 137 ÷ 52 = 2 remainder 33 |
| 4 | 52 ÷ 33 = 1 remainder 19 |
| 5 | 33 ÷ 19 = 1 remainder 14 |
| 6 | 19 ÷ 14 = 1 remainder 5 |
| 7 | 14 ÷ 5 = 2 remainder 4 |
| 8 | 5 ÷ 4 = 1 remainder 1 |
| 9 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 16 | 464 |
| 187 and 149 | 27863 |
| 125 and 109 | 13625 |
| 60 and 191 | 11460 |
| 75 and 20 | 300 |