Least Common Multiple (LCM) of 111 and 46
The least common multiple (LCM) of 111 and 46 is 5106.
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 46?
First, calculate the GCD of 111 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 46 = 2 remainder 19 |
| 2 | 46 ÷ 19 = 2 remainder 8 |
| 3 | 19 ÷ 8 = 2 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 103 | 13287 |
| 120 and 109 | 13080 |
| 80 and 145 | 2320 |
| 52 and 28 | 364 |
| 56 and 90 | 2520 |