Least Common Multiple (LCM) of 113 and 133
The least common multiple (LCM) of 113 and 133 is 15029.
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 133?
First, calculate the GCD of 113 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 133 = 0 remainder 113 |
| 2 | 133 ÷ 113 = 1 remainder 20 |
| 3 | 113 ÷ 20 = 5 remainder 13 |
| 4 | 20 ÷ 13 = 1 remainder 7 |
| 5 | 13 ÷ 7 = 1 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 105 | 420 |
| 36 and 12 | 36 |
| 129 and 186 | 7998 |
| 189 and 101 | 19089 |
| 42 and 21 | 42 |