Least Common Multiple (LCM) of 49 and 137
The least common multiple (LCM) of 49 and 137 is 6713.
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 49 and 137?
First, calculate the GCD of 49 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 137 = 0 remainder 49 |
| 2 | 137 ÷ 49 = 2 remainder 39 |
| 3 | 49 ÷ 39 = 1 remainder 10 |
| 4 | 39 ÷ 10 = 3 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 191 | 11078 |
| 189 and 106 | 20034 |
| 81 and 81 | 81 |
| 38 and 133 | 266 |
| 191 and 135 | 25785 |