Least Common Multiple (LCM) of 105 and 138
The least common multiple (LCM) of 105 and 138 is 4830.
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 105 and 138?
First, calculate the GCD of 105 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 138 = 0 remainder 105 |
| 2 | 138 ÷ 105 = 1 remainder 33 |
| 3 | 105 ÷ 33 = 3 remainder 6 |
| 4 | 33 ÷ 6 = 5 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 37 | 4625 |
| 78 and 105 | 2730 |
| 28 and 129 | 3612 |
| 106 and 18 | 954 |
| 57 and 103 | 5871 |