Least Common Multiple (LCM) of 137 and 195
The least common multiple (LCM) of 137 and 195 is 26715.
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 195?
First, calculate the GCD of 137 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 195 = 0 remainder 137 |
| 2 | 195 ÷ 137 = 1 remainder 58 |
| 3 | 137 ÷ 58 = 2 remainder 21 |
| 4 | 58 ÷ 21 = 2 remainder 16 |
| 5 | 21 ÷ 16 = 1 remainder 5 |
| 6 | 16 ÷ 5 = 3 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 112 | 1904 |
| 91 and 105 | 1365 |
| 42 and 113 | 4746 |
| 163 and 107 | 17441 |
| 117 and 37 | 4329 |