Least Common Multiple (LCM) of 194 and 120
The least common multiple (LCM) of 194 and 120 is 11640.
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 194 and 120?
First, calculate the GCD of 194 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 120 = 1 remainder 74 |
| 2 | 120 ÷ 74 = 1 remainder 46 |
| 3 | 74 ÷ 46 = 1 remainder 28 |
| 4 | 46 ÷ 28 = 1 remainder 18 |
| 5 | 28 ÷ 18 = 1 remainder 10 |
| 6 | 18 ÷ 10 = 1 remainder 8 |
| 7 | 10 ÷ 8 = 1 remainder 2 |
| 8 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 92 | 644 |
| 83 and 185 | 15355 |
| 169 and 114 | 19266 |
| 173 and 69 | 11937 |
| 80 and 67 | 5360 |