Least Common Multiple (LCM) of 99 and 104
The least common multiple (LCM) of 99 and 104 is 10296.
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 104?
First, calculate the GCD of 99 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 104 = 0 remainder 99 |
| 2 | 104 ÷ 99 = 1 remainder 5 |
| 3 | 99 ÷ 5 = 19 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 80 | 10320 |
| 146 and 84 | 6132 |
| 41 and 192 | 7872 |
| 123 and 176 | 21648 |
| 107 and 159 | 17013 |