Least Common Multiple (LCM) of 138 and 99
The least common multiple (LCM) of 138 and 99 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 138 and 99?
First, calculate the GCD of 138 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 99 = 1 remainder 39 |
| 2 | 99 ÷ 39 = 2 remainder 21 |
| 3 | 39 ÷ 21 = 1 remainder 18 |
| 4 | 21 ÷ 18 = 1 remainder 3 |
| 5 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 170 | 15470 |
| 186 and 183 | 11346 |
| 29 and 104 | 3016 |
| 78 and 193 | 15054 |
| 69 and 11 | 759 |