Least Common Multiple (LCM) of 78 and 111
The least common multiple (LCM) of 78 and 111 is 2886.
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 111?
First, calculate the GCD of 78 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 111 = 0 remainder 78 |
| 2 | 111 ÷ 78 = 1 remainder 33 |
| 3 | 78 ÷ 33 = 2 remainder 12 |
| 4 | 33 ÷ 12 = 2 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 153 | 30600 |
| 129 and 170 | 21930 |
| 88 and 82 | 3608 |
| 94 and 199 | 18706 |
| 116 and 107 | 12412 |