Least Common Multiple (LCM) of 27 and 102
The least common multiple (LCM) of 27 and 102 is 918.
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 102?
First, calculate the GCD of 27 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 102 = 0 remainder 27 |
| 2 | 102 ÷ 27 = 3 remainder 21 |
| 3 | 27 ÷ 21 = 1 remainder 6 |
| 4 | 21 ÷ 6 = 3 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 61 | 10919 |
| 165 and 35 | 1155 |
| 119 and 57 | 6783 |
| 37 and 100 | 3700 |
| 188 and 81 | 15228 |