Least Common Multiple (LCM) of 34 and 86
The least common multiple (LCM) of 34 and 86 is 1462.
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 34 and 86?
First, calculate the GCD of 34 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 86 = 0 remainder 34 |
| 2 | 86 ÷ 34 = 2 remainder 18 |
| 3 | 34 ÷ 18 = 1 remainder 16 |
| 4 | 18 ÷ 16 = 1 remainder 2 |
| 5 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 83 | 10624 |
| 150 and 26 | 1950 |
| 112 and 39 | 4368 |
| 36 and 174 | 1044 |
| 95 and 53 | 5035 |