Least Common Multiple (LCM) of 138 and 100
The least common multiple (LCM) of 138 and 100 is 6900.
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 100?
First, calculate the GCD of 138 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 100 = 1 remainder 38 |
| 2 | 100 ÷ 38 = 2 remainder 24 |
| 3 | 38 ÷ 24 = 1 remainder 14 |
| 4 | 24 ÷ 14 = 1 remainder 10 |
| 5 | 14 ÷ 10 = 1 remainder 4 |
| 6 | 10 ÷ 4 = 2 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 28 | 1344 |
| 185 and 199 | 36815 |
| 194 and 155 | 30070 |
| 145 and 83 | 12035 |
| 82 and 85 | 6970 |