Least Common Multiple (LCM) of 141 and 178
The least common multiple (LCM) of 141 and 178 is 25098.
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 141 and 178?
First, calculate the GCD of 141 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 141 ÷ 178 = 0 remainder 141 |
| 2 | 178 ÷ 141 = 1 remainder 37 |
| 3 | 141 ÷ 37 = 3 remainder 30 |
| 4 | 37 ÷ 30 = 1 remainder 7 |
| 5 | 30 ÷ 7 = 4 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 170 | 1870 |
| 87 and 160 | 13920 |
| 113 and 22 | 2486 |
| 178 and 181 | 32218 |
| 78 and 50 | 1950 |