Least Common Multiple (LCM) of 113 and 134
The least common multiple (LCM) of 113 and 134 is 15142.
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 134?
First, calculate the GCD of 113 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 134 = 0 remainder 113 |
| 2 | 134 ÷ 113 = 1 remainder 21 |
| 3 | 113 ÷ 21 = 5 remainder 8 |
| 4 | 21 ÷ 8 = 2 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 162 | 12960 |
| 105 and 128 | 13440 |
| 132 and 26 | 1716 |
| 123 and 53 | 6519 |
| 183 and 130 | 23790 |