Least Common Multiple (LCM) of 27 and 41
The least common multiple (LCM) of 27 and 41 is 1107.
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 41?
First, calculate the GCD of 27 and 41 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 41 = 0 remainder 27 |
| 2 | 41 ÷ 27 = 1 remainder 14 |
| 3 | 27 ÷ 14 = 1 remainder 13 |
| 4 | 14 ÷ 13 = 1 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 68 | 5236 |
| 111 and 134 | 14874 |
| 40 and 194 | 3880 |
| 77 and 65 | 5005 |
| 137 and 152 | 20824 |