Least Common Multiple (LCM) of 83 and 134
The least common multiple (LCM) of 83 and 134 is 11122.
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 83 and 134?
First, calculate the GCD of 83 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 134 = 0 remainder 83 |
| 2 | 134 ÷ 83 = 1 remainder 51 |
| 3 | 83 ÷ 51 = 1 remainder 32 |
| 4 | 51 ÷ 32 = 1 remainder 19 |
| 5 | 32 ÷ 19 = 1 remainder 13 |
| 6 | 19 ÷ 13 = 1 remainder 6 |
| 7 | 13 ÷ 6 = 2 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 164 | 1804 |
| 107 and 163 | 17441 |
| 130 and 200 | 2600 |
| 113 and 178 | 20114 |
| 68 and 30 | 1020 |