Least Common Multiple (LCM) of 134 and 71
The least common multiple (LCM) of 134 and 71 is 9514.
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 134 and 71?
First, calculate the GCD of 134 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 134 ÷ 71 = 1 remainder 63 |
| 2 | 71 ÷ 63 = 1 remainder 8 |
| 3 | 63 ÷ 8 = 7 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 125 | 23625 |
| 119 and 15 | 1785 |
| 199 and 105 | 20895 |
| 105 and 61 | 6405 |
| 107 and 129 | 13803 |