Least Common Multiple (LCM) of 113 and 82
The least common multiple (LCM) of 113 and 82 is 9266.
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 82?
First, calculate the GCD of 113 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 82 = 1 remainder 31 |
| 2 | 82 ÷ 31 = 2 remainder 20 |
| 3 | 31 ÷ 20 = 1 remainder 11 |
| 4 | 20 ÷ 11 = 1 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 152 | 7144 |
| 148 and 37 | 148 |
| 135 and 111 | 4995 |
| 128 and 42 | 2688 |
| 48 and 20 | 240 |