Least Common Multiple (LCM) of 111 and 141
The least common multiple (LCM) of 111 and 141 is 5217.
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 141?
First, calculate the GCD of 111 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 141 = 0 remainder 111 |
| 2 | 141 ÷ 111 = 1 remainder 30 |
| 3 | 111 ÷ 30 = 3 remainder 21 |
| 4 | 30 ÷ 21 = 1 remainder 9 |
| 5 | 21 ÷ 9 = 2 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 96 | 1632 |
| 62 and 136 | 4216 |
| 120 and 147 | 5880 |
| 28 and 14 | 28 |
| 84 and 128 | 2688 |