Least Common Multiple (LCM) of 105 and 78
The least common multiple (LCM) of 105 and 78 is 2730.
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 78?
First, calculate the GCD of 105 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 78 = 1 remainder 27 |
| 2 | 78 ÷ 27 = 2 remainder 24 |
| 3 | 27 ÷ 24 = 1 remainder 3 |
| 4 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 43 | 5418 |
| 133 and 145 | 19285 |
| 180 and 41 | 7380 |
| 63 and 121 | 7623 |
| 137 and 199 | 27263 |