Least Common Multiple (LCM) of 120 and 197
The least common multiple (LCM) of 120 and 197 is 23640.
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 197?
First, calculate the GCD of 120 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 197 = 0 remainder 120 |
| 2 | 197 ÷ 120 = 1 remainder 77 |
| 3 | 120 ÷ 77 = 1 remainder 43 |
| 4 | 77 ÷ 43 = 1 remainder 34 |
| 5 | 43 ÷ 34 = 1 remainder 9 |
| 6 | 34 ÷ 9 = 3 remainder 7 |
| 7 | 9 ÷ 7 = 1 remainder 2 |
| 8 | 7 ÷ 2 = 3 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 92 and 12 | 276 |
| 111 and 74 | 222 |
| 32 and 65 | 2080 |
| 50 and 108 | 2700 |
| 12 and 158 | 948 |