Least Common Multiple (LCM) of 113 and 137
The least common multiple (LCM) of 113 and 137 is 15481.
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 113 and 137?
First, calculate the GCD of 113 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 137 = 0 remainder 113 |
| 2 | 137 ÷ 113 = 1 remainder 24 |
| 3 | 113 ÷ 24 = 4 remainder 17 |
| 4 | 24 ÷ 17 = 1 remainder 7 |
| 5 | 17 ÷ 7 = 2 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 36 | 468 |
| 41 and 144 | 5904 |
| 59 and 128 | 7552 |
| 129 and 77 | 9933 |
| 140 and 40 | 280 |