Least Common Multiple (LCM) of 123 and 91
The least common multiple (LCM) of 123 and 91 is 11193.
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 123 and 91?
First, calculate the GCD of 123 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 91 = 1 remainder 32 |
| 2 | 91 ÷ 32 = 2 remainder 27 |
| 3 | 32 ÷ 27 = 1 remainder 5 |
| 4 | 27 ÷ 5 = 5 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 92 | 2024 |
| 192 and 12 | 192 |
| 200 and 165 | 6600 |
| 173 and 136 | 23528 |
| 73 and 175 | 12775 |