Least Common Multiple (LCM) of 113 and 111
The least common multiple (LCM) of 113 and 111 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 113 and 111?
First, calculate the GCD of 113 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 111 = 1 remainder 2 |
| 2 | 111 ÷ 2 = 55 remainder 1 |
| 3 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 98 | 980 |
| 166 and 101 | 16766 |
| 175 and 78 | 13650 |
| 76 and 79 | 6004 |
| 71 and 108 | 7668 |