Least Common Multiple (LCM) of 49 and 111
The least common multiple (LCM) of 49 and 111 is 5439.
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 49 and 111?
First, calculate the GCD of 49 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 111 = 0 remainder 49 |
| 2 | 111 ÷ 49 = 2 remainder 13 |
| 3 | 49 ÷ 13 = 3 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 182 | 1638 |
| 122 and 15 | 1830 |
| 84 and 132 | 924 |
| 192 and 93 | 5952 |
| 135 and 102 | 4590 |