Least Common Multiple (LCM) of 107 and 99
The least common multiple (LCM) of 107 and 99 is 10593.
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 107 and 99?
First, calculate the GCD of 107 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 99 = 1 remainder 8 |
| 2 | 99 ÷ 8 = 12 remainder 3 |
| 3 | 8 ÷ 3 = 2 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 65 | 3510 |
| 73 and 57 | 4161 |
| 45 and 42 | 630 |
| 50 and 72 | 1800 |
| 196 and 55 | 10780 |