Least Common Multiple (LCM) of 99 and 121
The least common multiple (LCM) of 99 and 121 is 1089.
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 121?
First, calculate the GCD of 99 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 121 = 0 remainder 99 |
| 2 | 121 ÷ 99 = 1 remainder 22 |
| 3 | 99 ÷ 22 = 4 remainder 11 |
| 4 | 22 ÷ 11 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 36 | 36 |
| 100 and 84 | 2100 |
| 144 and 103 | 14832 |
| 36 and 180 | 180 |
| 13 and 25 | 325 |