Least Common Multiple (LCM) of 120 and 194
The least common multiple (LCM) of 120 and 194 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 120 and 194?
First, calculate the GCD of 120 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 194 = 0 remainder 120 |
| 2 | 194 ÷ 120 = 1 remainder 74 |
| 3 | 120 ÷ 74 = 1 remainder 46 |
| 4 | 74 ÷ 46 = 1 remainder 28 |
| 5 | 46 ÷ 28 = 1 remainder 18 |
| 6 | 28 ÷ 18 = 1 remainder 10 |
| 7 | 18 ÷ 10 = 1 remainder 8 |
| 8 | 10 ÷ 8 = 1 remainder 2 |
| 9 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 70 | 490 |
| 100 and 66 | 3300 |
| 185 and 160 | 5920 |
| 85 and 174 | 14790 |
| 103 and 120 | 12360 |