Least Common Multiple (LCM) of 89 and 140
The least common multiple (LCM) of 89 and 140 is 12460.
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 89 and 140?
First, calculate the GCD of 89 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 140 = 0 remainder 89 |
| 2 | 140 ÷ 89 = 1 remainder 51 |
| 3 | 89 ÷ 51 = 1 remainder 38 |
| 4 | 51 ÷ 38 = 1 remainder 13 |
| 5 | 38 ÷ 13 = 2 remainder 12 |
| 6 | 13 ÷ 12 = 1 remainder 1 |
| 7 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 51 | 2346 |
| 129 and 175 | 22575 |
| 189 and 45 | 945 |
| 145 and 24 | 3480 |
| 78 and 108 | 1404 |