Least Common Multiple (LCM) of 27 and 114
The least common multiple (LCM) of 27 and 114 is 1026.
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 114?
First, calculate the GCD of 27 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 114 = 0 remainder 27 |
| 2 | 114 ÷ 27 = 4 remainder 6 |
| 3 | 27 ÷ 6 = 4 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 49 | 7595 |
| 33 and 109 | 3597 |
| 53 and 198 | 10494 |
| 59 and 113 | 6667 |
| 83 and 13 | 1079 |