Least Common Multiple (LCM) of 113 and 123
The least common multiple (LCM) of 113 and 123 is 13899.
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 123?
First, calculate the GCD of 113 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 123 = 0 remainder 113 |
| 2 | 123 ÷ 113 = 1 remainder 10 |
| 3 | 113 ÷ 10 = 11 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 72 | 6408 |
| 37 and 183 | 6771 |
| 75 and 132 | 3300 |
| 152 and 167 | 25384 |
| 97 and 107 | 10379 |