Least Common Multiple (LCM) of 113 and 139
The least common multiple (LCM) of 113 and 139 is 15707.
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 139?
First, calculate the GCD of 113 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 139 = 0 remainder 113 |
| 2 | 139 ÷ 113 = 1 remainder 26 |
| 3 | 113 ÷ 26 = 4 remainder 9 |
| 4 | 26 ÷ 9 = 2 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 200 | 22600 |
| 155 and 200 | 6200 |
| 50 and 54 | 1350 |
| 42 and 77 | 462 |
| 54 and 162 | 162 |