Least Common Multiple (LCM) of 99 and 139
The least common multiple (LCM) of 99 and 139 is 13761.
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 139?
First, calculate the GCD of 99 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 139 = 0 remainder 99 |
| 2 | 139 ÷ 99 = 1 remainder 40 |
| 3 | 99 ÷ 40 = 2 remainder 19 |
| 4 | 40 ÷ 19 = 2 remainder 2 |
| 5 | 19 ÷ 2 = 9 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 95 | 11685 |
| 83 and 122 | 10126 |
| 147 and 40 | 5880 |
| 177 and 131 | 23187 |
| 13 and 39 | 39 |