Least Common Multiple (LCM) of 123 and 113
The least common multiple (LCM) of 123 and 113 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 123 and 113?
First, calculate the GCD of 123 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 113 = 1 remainder 10 |
| 2 | 113 ÷ 10 = 11 remainder 3 |
| 3 | 10 ÷ 3 = 3 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 143 | 19877 |
| 39 and 198 | 2574 |
| 15 and 35 | 105 |
| 115 and 167 | 19205 |
| 190 and 146 | 13870 |