Least Common Multiple (LCM) of 122 and 67
The least common multiple (LCM) of 122 and 67 is 8174.
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 67?
First, calculate the GCD of 122 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 67 = 1 remainder 55 |
| 2 | 67 ÷ 55 = 1 remainder 12 |
| 3 | 55 ÷ 12 = 4 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 22 | 1606 |
| 185 and 110 | 4070 |
| 152 and 92 | 3496 |
| 10 and 165 | 330 |
| 122 and 58 | 3538 |