Least Common Multiple (LCM) of 71 and 134
The least common multiple (LCM) of 71 and 134 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 71 and 134?
First, calculate the GCD of 71 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 134 = 0 remainder 71 |
| 2 | 134 ÷ 71 = 1 remainder 63 |
| 3 | 71 ÷ 63 = 1 remainder 8 |
| 4 | 63 ÷ 8 = 7 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 54 | 4158 |
| 39 and 190 | 7410 |
| 45 and 73 | 3285 |
| 109 and 154 | 16786 |
| 83 and 78 | 6474 |