Least Common Multiple (LCM) of 27 and 69
The least common multiple (LCM) of 27 and 69 is 621.
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 69?
First, calculate the GCD of 27 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 69 = 0 remainder 27 |
| 2 | 69 ÷ 27 = 2 remainder 15 |
| 3 | 27 ÷ 15 = 1 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 92 | 10948 |
| 108 and 78 | 1404 |
| 157 and 166 | 26062 |
| 168 and 13 | 2184 |
| 96 and 158 | 7584 |