Least Common Multiple (LCM) of 122 and 113
The least common multiple (LCM) of 122 and 113 is 13786.
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 113?
First, calculate the GCD of 122 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 113 = 1 remainder 9 |
| 2 | 113 ÷ 9 = 12 remainder 5 |
| 3 | 9 ÷ 5 = 1 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 45 | 1845 |
| 167 and 135 | 22545 |
| 164 and 133 | 21812 |
| 16 and 84 | 336 |
| 173 and 74 | 12802 |