Least Common Multiple (LCM) of 60 and 198
The least common multiple (LCM) of 60 and 198 is 1980.
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 198?
First, calculate the GCD of 60 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 198 = 0 remainder 60 |
| 2 | 198 ÷ 60 = 3 remainder 18 |
| 3 | 60 ÷ 18 = 3 remainder 6 |
| 4 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 40 | 4840 |
| 22 and 48 | 528 |
| 120 and 177 | 7080 |
| 117 and 69 | 2691 |
| 174 and 20 | 1740 |