Least Common Multiple (LCM) of 30 and 86
The least common multiple (LCM) of 30 and 86 is 1290.
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 30 and 86?
First, calculate the GCD of 30 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 86 = 0 remainder 30 |
| 2 | 86 ÷ 30 = 2 remainder 26 |
| 3 | 30 ÷ 26 = 1 remainder 4 |
| 4 | 26 ÷ 4 = 6 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 108 | 5724 |
| 27 and 29 | 783 |
| 134 and 157 | 21038 |
| 142 and 63 | 8946 |
| 13 and 121 | 1573 |