Least Common Multiple (LCM) of 99 and 55
The least common multiple (LCM) of 99 and 55 is 495.
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 55?
First, calculate the GCD of 99 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 55 = 1 remainder 44 |
| 2 | 55 ÷ 44 = 1 remainder 11 |
| 3 | 44 ÷ 11 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 64 | 8256 |
| 189 and 181 | 34209 |
| 179 and 48 | 8592 |
| 135 and 120 | 1080 |
| 45 and 113 | 5085 |