Least Common Multiple (LCM) of 41 and 178
The least common multiple (LCM) of 41 and 178 is 7298.
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 41 and 178?
First, calculate the GCD of 41 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 41 ÷ 178 = 0 remainder 41 |
| 2 | 178 ÷ 41 = 4 remainder 14 |
| 3 | 41 ÷ 14 = 2 remainder 13 |
| 4 | 14 ÷ 13 = 1 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 68 | 13396 |
| 27 and 22 | 594 |
| 114 and 70 | 3990 |
| 19 and 90 | 1710 |
| 103 and 157 | 16171 |