Least Common Multiple (LCM) of 109 and 99
The least common multiple (LCM) of 109 and 99 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 109 and 99?
First, calculate the GCD of 109 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 99 = 1 remainder 10 |
| 2 | 99 ÷ 10 = 9 remainder 9 |
| 3 | 10 ÷ 9 = 1 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 45 | 2070 |
| 74 and 110 | 4070 |
| 53 and 113 | 5989 |
| 144 and 176 | 1584 |
| 194 and 15 | 2910 |