Least Common Multiple (LCM) of 117 and 122
The least common multiple (LCM) of 117 and 122 is 14274.
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 117 and 122?
First, calculate the GCD of 117 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 122 = 0 remainder 117 |
| 2 | 122 ÷ 117 = 1 remainder 5 |
| 3 | 117 ÷ 5 = 23 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 132 | 8316 |
| 29 and 131 | 3799 |
| 144 and 139 | 20016 |
| 141 and 11 | 1551 |
| 19 and 188 | 3572 |