Least Common Multiple (LCM) of 27 and 30
The least common multiple (LCM) of 27 and 30 is 270.
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 27 and 30?
First, calculate the GCD of 27 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 30 = 0 remainder 27 |
| 2 | 30 ÷ 27 = 1 remainder 3 |
| 3 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 80 | 2000 |
| 166 and 138 | 11454 |
| 193 and 18 | 3474 |
| 94 and 51 | 4794 |
| 180 and 188 | 8460 |