Least Common Multiple (LCM) of 115 and 140
The least common multiple (LCM) of 115 and 140 is 3220.
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 115 and 140?
First, calculate the GCD of 115 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 140 = 0 remainder 115 |
| 2 | 140 ÷ 115 = 1 remainder 25 |
| 3 | 115 ÷ 25 = 4 remainder 15 |
| 4 | 25 ÷ 15 = 1 remainder 10 |
| 5 | 15 ÷ 10 = 1 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 20 | 580 |
| 117 and 63 | 819 |
| 150 and 138 | 3450 |
| 65 and 17 | 1105 |
| 80 and 65 | 1040 |