Least Common Multiple (LCM) of 140 and 89
The least common multiple (LCM) of 140 and 89 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 140 and 89?
First, calculate the GCD of 140 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 89 = 1 remainder 51 |
| 2 | 89 ÷ 51 = 1 remainder 38 |
| 3 | 51 ÷ 38 = 1 remainder 13 |
| 4 | 38 ÷ 13 = 2 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 23 | 2208 |
| 58 and 194 | 5626 |
| 138 and 24 | 552 |
| 139 and 190 | 26410 |
| 178 and 121 | 21538 |