Least Common Multiple (LCM) of 111 and 140
The least common multiple (LCM) of 111 and 140 is 15540.
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 111 and 140?
First, calculate the GCD of 111 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 140 = 0 remainder 111 |
| 2 | 140 ÷ 111 = 1 remainder 29 |
| 3 | 111 ÷ 29 = 3 remainder 24 |
| 4 | 29 ÷ 24 = 1 remainder 5 |
| 5 | 24 ÷ 5 = 4 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 149 | 21456 |
| 170 and 105 | 3570 |
| 172 and 46 | 3956 |
| 45 and 10 | 90 |
| 186 and 19 | 3534 |