Least Common Multiple (LCM) of 78 and 105
The least common multiple (LCM) of 78 and 105 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 78 and 105?
First, calculate the GCD of 78 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 105 = 0 remainder 78 |
| 2 | 105 ÷ 78 = 1 remainder 27 |
| 3 | 78 ÷ 27 = 2 remainder 24 |
| 4 | 27 ÷ 24 = 1 remainder 3 |
| 5 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 129 | 774 |
| 98 and 59 | 5782 |
| 136 and 77 | 10472 |
| 77 and 77 | 77 |
| 112 and 141 | 15792 |