Least Common Multiple (LCM) of 111 and 113
The least common multiple (LCM) of 111 and 113 is 12543.
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 113?
First, calculate the GCD of 111 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 113 = 0 remainder 111 |
| 2 | 113 ÷ 111 = 1 remainder 2 |
| 3 | 111 ÷ 2 = 55 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 87 | 11397 |
| 200 and 58 | 5800 |
| 163 and 109 | 17767 |
| 129 and 135 | 5805 |
| 50 and 57 | 2850 |