Least Common Multiple (LCM) of 30 and 89
The least common multiple (LCM) of 30 and 89 is 2670.
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 89?
First, calculate the GCD of 30 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 89 = 0 remainder 30 |
| 2 | 89 ÷ 30 = 2 remainder 29 |
| 3 | 30 ÷ 29 = 1 remainder 1 |
| 4 | 29 ÷ 1 = 29 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 186 | 14694 |
| 32 and 13 | 416 |
| 61 and 195 | 11895 |
| 78 and 132 | 1716 |
| 108 and 43 | 4644 |