Least Common Multiple (LCM) of 122 and 165
The least common multiple (LCM) of 122 and 165 is 20130.
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 165?
First, calculate the GCD of 122 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 165 = 0 remainder 122 |
| 2 | 165 ÷ 122 = 1 remainder 43 |
| 3 | 122 ÷ 43 = 2 remainder 36 |
| 4 | 43 ÷ 36 = 1 remainder 7 |
| 5 | 36 ÷ 7 = 5 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 88 | 13112 |
| 142 and 80 | 5680 |
| 180 and 115 | 4140 |
| 104 and 196 | 5096 |
| 32 and 183 | 5856 |