Least Common Multiple (LCM) of 122 and 178
The least common multiple (LCM) of 122 and 178 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 122 and 178?
First, calculate the GCD of 122 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 178 = 0 remainder 122 |
| 2 | 178 ÷ 122 = 1 remainder 56 |
| 3 | 122 ÷ 56 = 2 remainder 10 |
| 4 | 56 ÷ 10 = 5 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 79 and 167 | 13193 |
| 197 and 74 | 14578 |
| 30 and 125 | 750 |
| 110 and 109 | 11990 |
| 15 and 144 | 720 |