Least Common Multiple (LCM) of 113 and 83
The least common multiple (LCM) of 113 and 83 is 9379.
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 83?
First, calculate the GCD of 113 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 83 = 1 remainder 30 |
| 2 | 83 ÷ 30 = 2 remainder 23 |
| 3 | 30 ÷ 23 = 1 remainder 7 |
| 4 | 23 ÷ 7 = 3 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 195 | 390 |
| 96 and 135 | 4320 |
| 146 and 137 | 20002 |
| 162 and 105 | 5670 |
| 170 and 51 | 510 |