Least Common Multiple (LCM) of 199 and 78
The least common multiple (LCM) of 199 and 78 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 199 and 78?
First, calculate the GCD of 199 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 78 = 2 remainder 43 |
| 2 | 78 ÷ 43 = 1 remainder 35 |
| 3 | 43 ÷ 35 = 1 remainder 8 |
| 4 | 35 ÷ 8 = 4 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 70 | 1330 |
| 67 and 200 | 13400 |
| 109 and 48 | 5232 |
| 124 and 121 | 15004 |
| 99 and 92 | 9108 |