Least Common Multiple (LCM) of 86 and 138
The least common multiple (LCM) of 86 and 138 is 5934.
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 86 and 138?
First, calculate the GCD of 86 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 86 ÷ 138 = 0 remainder 86 |
| 2 | 138 ÷ 86 = 1 remainder 52 |
| 3 | 86 ÷ 52 = 1 remainder 34 |
| 4 | 52 ÷ 34 = 1 remainder 18 |
| 5 | 34 ÷ 18 = 1 remainder 16 |
| 6 | 18 ÷ 16 = 1 remainder 2 |
| 7 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 60 | 420 |
| 162 and 181 | 29322 |
| 53 and 188 | 9964 |
| 39 and 192 | 2496 |
| 45 and 38 | 1710 |