Least Common Multiple (LCM) of 178 and 122
The least common multiple (LCM) of 178 and 122 is 10858.
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 178 and 122?
First, calculate the GCD of 178 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 122 = 1 remainder 56 |
| 2 | 122 ÷ 56 = 2 remainder 10 |
| 3 | 56 ÷ 10 = 5 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 49 | 98 |
| 168 and 161 | 3864 |
| 141 and 76 | 10716 |
| 125 and 165 | 4125 |
| 31 and 84 | 2604 |