Least Common Multiple (LCM) of 78 and 107
The least common multiple (LCM) of 78 and 107 is 8346.
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 107?
First, calculate the GCD of 78 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 107 = 0 remainder 78 |
| 2 | 107 ÷ 78 = 1 remainder 29 |
| 3 | 78 ÷ 29 = 2 remainder 20 |
| 4 | 29 ÷ 20 = 1 remainder 9 |
| 5 | 20 ÷ 9 = 2 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 121 | 18755 |
| 106 and 36 | 1908 |
| 182 and 55 | 10010 |
| 183 and 147 | 8967 |
| 165 and 31 | 5115 |