Least Common Multiple (LCM) of 137 and 188
The least common multiple (LCM) of 137 and 188 is 25756.
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 188?
First, calculate the GCD of 137 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 188 = 0 remainder 137 |
| 2 | 188 ÷ 137 = 1 remainder 51 |
| 3 | 137 ÷ 51 = 2 remainder 35 |
| 4 | 51 ÷ 35 = 1 remainder 16 |
| 5 | 35 ÷ 16 = 2 remainder 3 |
| 6 | 16 ÷ 3 = 5 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 32 | 192 |
| 157 and 128 | 20096 |
| 188 and 149 | 28012 |
| 57 and 49 | 2793 |
| 185 and 185 | 185 |