Least Common Multiple (LCM) of 99 and 122
The least common multiple (LCM) of 99 and 122 is 12078.
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 99 and 122?
First, calculate the GCD of 99 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 122 = 0 remainder 99 |
| 2 | 122 ÷ 99 = 1 remainder 23 |
| 3 | 99 ÷ 23 = 4 remainder 7 |
| 4 | 23 ÷ 7 = 3 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 110 | 3740 |
| 63 and 191 | 12033 |
| 52 and 87 | 4524 |
| 112 and 157 | 17584 |
| 123 and 138 | 5658 |