Least Common Multiple (LCM) of 137 and 41
The least common multiple (LCM) of 137 and 41 is 5617.
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 41?
First, calculate the GCD of 137 and 41 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 41 = 3 remainder 14 |
| 2 | 41 ÷ 14 = 2 remainder 13 |
| 3 | 14 ÷ 13 = 1 remainder 1 |
| 4 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 113 | 113 |
| 165 and 91 | 15015 |
| 159 and 50 | 7950 |
| 89 and 127 | 11303 |
| 129 and 24 | 1032 |