Least Common Multiple (LCM) of 60 and 197
The least common multiple (LCM) of 60 and 197 is 11820.
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 60 and 197?
First, calculate the GCD of 60 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 197 = 0 remainder 60 |
| 2 | 197 ÷ 60 = 3 remainder 17 |
| 3 | 60 ÷ 17 = 3 remainder 9 |
| 4 | 17 ÷ 9 = 1 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 30 | 2220 |
| 67 and 133 | 8911 |
| 57 and 111 | 2109 |
| 137 and 67 | 9179 |
| 142 and 80 | 5680 |