Least Common Multiple (LCM) of 122 and 101
The least common multiple (LCM) of 122 and 101 is 12322.
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 101?
First, calculate the GCD of 122 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 101 = 1 remainder 21 |
| 2 | 101 ÷ 21 = 4 remainder 17 |
| 3 | 21 ÷ 17 = 1 remainder 4 |
| 4 | 17 ÷ 4 = 4 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 114 | 2394 |
| 170 and 30 | 510 |
| 19 and 60 | 1140 |
| 174 and 77 | 13398 |
| 111 and 107 | 11877 |