Least Common Multiple (LCM) of 111 and 91
The least common multiple (LCM) of 111 and 91 is 10101.
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 91?
First, calculate the GCD of 111 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 91 = 1 remainder 20 |
| 2 | 91 ÷ 20 = 4 remainder 11 |
| 3 | 20 ÷ 11 = 1 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 63 | 8190 |
| 47 and 101 | 4747 |
| 108 and 58 | 3132 |
| 173 and 121 | 20933 |
| 150 and 104 | 7800 |