Least Common Multiple (LCM) of 122 and 71
The least common multiple (LCM) of 122 and 71 is 8662.
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 71?
First, calculate the GCD of 122 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 71 = 1 remainder 51 |
| 2 | 71 ÷ 51 = 1 remainder 20 |
| 3 | 51 ÷ 20 = 2 remainder 11 |
| 4 | 20 ÷ 11 = 1 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 35 | 4935 |
| 58 and 124 | 3596 |
| 85 and 65 | 1105 |
| 176 and 80 | 880 |
| 34 and 29 | 986 |