Least Common Multiple (LCM) of 189 and 137
The least common multiple (LCM) of 189 and 137 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 189 and 137?
First, calculate the GCD of 189 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 137 = 1 remainder 52 |
| 2 | 137 ÷ 52 = 2 remainder 33 |
| 3 | 52 ÷ 33 = 1 remainder 19 |
| 4 | 33 ÷ 19 = 1 remainder 14 |
| 5 | 19 ÷ 14 = 1 remainder 5 |
| 6 | 14 ÷ 5 = 2 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 58 | 6554 |
| 137 and 102 | 13974 |
| 109 and 114 | 12426 |
| 126 and 121 | 15246 |
| 192 and 156 | 2496 |