Least Common Multiple (LCM) of 11 and 99
The least common multiple (LCM) of 11 and 99 is 99.
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 11 and 99?
First, calculate the GCD of 11 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 11 ÷ 99 = 0 remainder 11 |
| 2 | 99 ÷ 11 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 70 | 560 |
| 102 and 171 | 5814 |
| 180 and 191 | 34380 |
| 50 and 184 | 4600 |
| 182 and 108 | 9828 |