Least Common Multiple (LCM) of 111 and 192
The least common multiple (LCM) of 111 and 192 is 7104.
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 192?
First, calculate the GCD of 111 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 192 = 0 remainder 111 |
| 2 | 192 ÷ 111 = 1 remainder 81 |
| 3 | 111 ÷ 81 = 1 remainder 30 |
| 4 | 81 ÷ 30 = 2 remainder 21 |
| 5 | 30 ÷ 21 = 1 remainder 9 |
| 6 | 21 ÷ 9 = 2 remainder 3 |
| 7 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 69 | 9453 |
| 36 and 158 | 2844 |
| 104 and 124 | 3224 |
| 78 and 128 | 4992 |
| 54 and 126 | 378 |