Least Common Multiple (LCM) of 99 and 109
The least common multiple (LCM) of 99 and 109 is 10791.
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 109?
First, calculate the GCD of 99 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 109 = 0 remainder 99 |
| 2 | 109 ÷ 99 = 1 remainder 10 |
| 3 | 99 ÷ 10 = 9 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 181 | 20091 |
| 180 and 118 | 10620 |
| 98 and 102 | 4998 |
| 161 and 21 | 483 |
| 51 and 33 | 561 |