Least Common Multiple (LCM) of 111 and 67
The least common multiple (LCM) of 111 and 67 is 7437.
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 67?
First, calculate the GCD of 111 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 67 = 1 remainder 44 |
| 2 | 67 ÷ 44 = 1 remainder 23 |
| 3 | 44 ÷ 23 = 1 remainder 21 |
| 4 | 23 ÷ 21 = 1 remainder 2 |
| 5 | 21 ÷ 2 = 10 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 61 | 10492 |
| 41 and 154 | 6314 |
| 107 and 185 | 19795 |
| 174 and 181 | 31494 |
| 101 and 125 | 12625 |