Least Common Multiple (LCM) of 189 and 140
The least common multiple (LCM) of 189 and 140 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 140?
First, calculate the GCD of 189 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 140 = 1 remainder 49 |
| 2 | 140 ÷ 49 = 2 remainder 42 |
| 3 | 49 ÷ 42 = 1 remainder 7 |
| 4 | 42 ÷ 7 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 99 | 792 |
| 29 and 33 | 957 |
| 107 and 26 | 2782 |
| 54 and 68 | 1836 |
| 193 and 33 | 6369 |