Least Common Multiple (LCM) of 99 and 138
The least common multiple (LCM) of 99 and 138 is 4554.
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 138?
First, calculate the GCD of 99 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 138 = 0 remainder 99 |
| 2 | 138 ÷ 99 = 1 remainder 39 |
| 3 | 99 ÷ 39 = 2 remainder 21 |
| 4 | 39 ÷ 21 = 1 remainder 18 |
| 5 | 21 ÷ 18 = 1 remainder 3 |
| 6 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 92 | 10212 |
| 140 and 57 | 7980 |
| 91 and 200 | 18200 |
| 25 and 73 | 1825 |
| 186 and 122 | 11346 |