Least Common Multiple (LCM) of 111 and 61
The least common multiple (LCM) of 111 and 61 is 6771.
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 61?
First, calculate the GCD of 111 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 61 = 1 remainder 50 |
| 2 | 61 ÷ 50 = 1 remainder 11 |
| 3 | 50 ÷ 11 = 4 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 135 | 135 |
| 84 and 77 | 924 |
| 150 and 117 | 5850 |
| 25 and 34 | 850 |
| 141 and 74 | 10434 |