Least Common Multiple (LCM) of 137 and 113
The least common multiple (LCM) of 137 and 113 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 137 and 113?
First, calculate the GCD of 137 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 113 = 1 remainder 24 |
| 2 | 113 ÷ 24 = 4 remainder 17 |
| 3 | 24 ÷ 17 = 1 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 132 | 25476 |
| 155 and 76 | 11780 |
| 48 and 22 | 528 |
| 129 and 171 | 7353 |
| 190 and 73 | 13870 |