Least Common Multiple (LCM) of 33 and 122
The least common multiple (LCM) of 33 and 122 is 4026.
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 33 and 122?
First, calculate the GCD of 33 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 122 = 0 remainder 33 |
| 2 | 122 ÷ 33 = 3 remainder 23 |
| 3 | 33 ÷ 23 = 1 remainder 10 |
| 4 | 23 ÷ 10 = 2 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 133 | 16226 |
| 13 and 101 | 1313 |
| 91 and 97 | 8827 |
| 83 and 22 | 1826 |
| 83 and 116 | 9628 |