Least Common Multiple (LCM) of 78 and 199
The least common multiple (LCM) of 78 and 199 is 15522.
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 199?
First, calculate the GCD of 78 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 199 = 0 remainder 78 |
| 2 | 199 ÷ 78 = 2 remainder 43 |
| 3 | 78 ÷ 43 = 1 remainder 35 |
| 4 | 43 ÷ 35 = 1 remainder 8 |
| 5 | 35 ÷ 8 = 4 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 163 | 19071 |
| 25 and 108 | 2700 |
| 105 and 49 | 735 |
| 25 and 194 | 4850 |
| 65 and 70 | 910 |