Least Common Multiple (LCM) of 31 and 137
The least common multiple (LCM) of 31 and 137 is 4247.
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 31 and 137?
First, calculate the GCD of 31 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 137 = 0 remainder 31 |
| 2 | 137 ÷ 31 = 4 remainder 13 |
| 3 | 31 ÷ 13 = 2 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 36 | 1260 |
| 198 and 200 | 19800 |
| 67 and 51 | 3417 |
| 27 and 172 | 4644 |
| 64 and 158 | 5056 |