Least Common Multiple (LCM) of 113 and 124
The least common multiple (LCM) of 113 and 124 is 14012.
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 124?
First, calculate the GCD of 113 and 124 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 124 = 0 remainder 113 |
| 2 | 124 ÷ 113 = 1 remainder 11 |
| 3 | 113 ÷ 11 = 10 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 105 | 10920 |
| 138 and 175 | 24150 |
| 171 and 134 | 22914 |
| 22 and 84 | 924 |
| 87 and 186 | 5394 |