Least Common Multiple (LCM) of 99 and 83
The least common multiple (LCM) of 99 and 83 is 8217.
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 83?
First, calculate the GCD of 99 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 83 = 1 remainder 16 |
| 2 | 83 ÷ 16 = 5 remainder 3 |
| 3 | 16 ÷ 3 = 5 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 114 | 8778 |
| 130 and 25 | 650 |
| 88 and 100 | 2200 |
| 27 and 154 | 4158 |
| 103 and 140 | 14420 |