Least Common Multiple (LCM) of 113 and 184
The least common multiple (LCM) of 113 and 184 is 20792.
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 184?
First, calculate the GCD of 113 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 184 = 0 remainder 113 |
| 2 | 184 ÷ 113 = 1 remainder 71 |
| 3 | 113 ÷ 71 = 1 remainder 42 |
| 4 | 71 ÷ 42 = 1 remainder 29 |
| 5 | 42 ÷ 29 = 1 remainder 13 |
| 6 | 29 ÷ 13 = 2 remainder 3 |
| 7 | 13 ÷ 3 = 4 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 13 | 1092 |
| 65 and 187 | 12155 |
| 34 and 63 | 2142 |
| 125 and 31 | 3875 |
| 60 and 15 | 60 |