Least Common Multiple (LCM) of 91 and 111
The least common multiple (LCM) of 91 and 111 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 91 and 111?
First, calculate the GCD of 91 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 111 = 0 remainder 91 |
| 2 | 111 ÷ 91 = 1 remainder 20 |
| 3 | 91 ÷ 20 = 4 remainder 11 |
| 4 | 20 ÷ 11 = 1 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 110 | 110 |
| 111 and 124 | 13764 |
| 132 and 175 | 23100 |
| 79 and 65 | 5135 |
| 199 and 34 | 6766 |