Least Common Multiple (LCM) of 113 and 183
The least common multiple (LCM) of 113 and 183 is 20679.
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 183?
First, calculate the GCD of 113 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 183 = 0 remainder 113 |
| 2 | 183 ÷ 113 = 1 remainder 70 |
| 3 | 113 ÷ 70 = 1 remainder 43 |
| 4 | 70 ÷ 43 = 1 remainder 27 |
| 5 | 43 ÷ 27 = 1 remainder 16 |
| 6 | 27 ÷ 16 = 1 remainder 11 |
| 7 | 16 ÷ 11 = 1 remainder 5 |
| 8 | 11 ÷ 5 = 2 remainder 1 |
| 9 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 119 | 1666 |
| 29 and 69 | 2001 |
| 119 and 35 | 595 |
| 198 and 69 | 4554 |
| 16 and 62 | 496 |