Least Common Multiple (LCM) of 189 and 60
The least common multiple (LCM) of 189 and 60 is 3780.
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 189 and 60?
First, calculate the GCD of 189 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 60 = 3 remainder 9 |
| 2 | 60 ÷ 9 = 6 remainder 6 |
| 3 | 9 ÷ 6 = 1 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 45 | 3195 |
| 167 and 35 | 5845 |
| 90 and 29 | 2610 |
| 14 and 62 | 434 |
| 119 and 74 | 8806 |