Least Common Multiple (LCM) of 27 and 178
The least common multiple (LCM) of 27 and 178 is 4806.
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 178?
First, calculate the GCD of 27 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 178 = 0 remainder 27 |
| 2 | 178 ÷ 27 = 6 remainder 16 |
| 3 | 27 ÷ 16 = 1 remainder 11 |
| 4 | 16 ÷ 11 = 1 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 102 | 408 |
| 113 and 51 | 5763 |
| 100 and 194 | 9700 |
| 186 and 114 | 3534 |
| 141 and 181 | 25521 |