Least Common Multiple (LCM) of 78 and 191
The least common multiple (LCM) of 78 and 191 is 14898.
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 191?
First, calculate the GCD of 78 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 191 = 0 remainder 78 |
| 2 | 191 ÷ 78 = 2 remainder 35 |
| 3 | 78 ÷ 35 = 2 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 |
|---|---|
| 84 and 160 | 3360 |
| 151 and 165 | 24915 |
| 48 and 55 | 2640 |
| 153 and 123 | 6273 |
| 164 and 140 | 5740 |