Least Common Multiple (LCM) of 113 and 140
The least common multiple (LCM) of 113 and 140 is 15820.
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 113 and 140?
First, calculate the GCD of 113 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 140 = 0 remainder 113 |
| 2 | 140 ÷ 113 = 1 remainder 27 |
| 3 | 113 ÷ 27 = 4 remainder 5 |
| 4 | 27 ÷ 5 = 5 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 148 | 15540 |
| 107 and 65 | 6955 |
| 159 and 12 | 636 |
| 12 and 186 | 372 |
| 70 and 61 | 4270 |