Least Common Multiple (LCM) of 27 and 38
The least common multiple (LCM) of 27 and 38 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 38?
First, calculate the GCD of 27 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 38 = 0 remainder 27 |
| 2 | 38 ÷ 27 = 1 remainder 11 |
| 3 | 27 ÷ 11 = 2 remainder 5 |
| 4 | 11 ÷ 5 = 2 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 20 | 1340 |
| 71 and 107 | 7597 |
| 64 and 18 | 576 |
| 114 and 174 | 3306 |
| 16 and 43 | 688 |