Least Common Multiple (LCM) of 140 and 189
The least common multiple (LCM) of 140 and 189 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 140 and 189?
First, calculate the GCD of 140 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 189 = 0 remainder 140 |
| 2 | 189 ÷ 140 = 1 remainder 49 |
| 3 | 140 ÷ 49 = 2 remainder 42 |
| 4 | 49 ÷ 42 = 1 remainder 7 |
| 5 | 42 ÷ 7 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 169 | 10816 |
| 176 and 78 | 6864 |
| 110 and 77 | 770 |
| 29 and 172 | 4988 |
| 123 and 114 | 4674 |