Least Common Multiple (LCM) of 99 and 110
The least common multiple (LCM) of 99 and 110 is 990.
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 110?
First, calculate the GCD of 99 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 110 = 0 remainder 99 |
| 2 | 110 ÷ 99 = 1 remainder 11 |
| 3 | 99 ÷ 11 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 57 | 1767 |
| 37 and 19 | 703 |
| 193 and 54 | 10422 |
| 19 and 114 | 114 |
| 170 and 123 | 20910 |