Least Common Multiple (LCM) of 27 and 49
The least common multiple (LCM) of 27 and 49 is 1323.
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 49?
First, calculate the GCD of 27 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 49 = 0 remainder 27 |
| 2 | 49 ÷ 27 = 1 remainder 22 |
| 3 | 27 ÷ 22 = 1 remainder 5 |
| 4 | 22 ÷ 5 = 4 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 96 | 864 |
| 199 and 62 | 12338 |
| 138 and 58 | 4002 |
| 67 and 131 | 8777 |
| 200 and 182 | 18200 |