Least Common Multiple (LCM) of 27 and 71
The least common multiple (LCM) of 27 and 71 is 1917.
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 71?
First, calculate the GCD of 27 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 71 = 0 remainder 27 |
| 2 | 71 ÷ 27 = 2 remainder 17 |
| 3 | 27 ÷ 17 = 1 remainder 10 |
| 4 | 17 ÷ 10 = 1 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 189 | 21735 |
| 92 and 15 | 1380 |
| 15 and 122 | 1830 |
| 10 and 64 | 320 |
| 105 and 186 | 6510 |