Least Common Multiple (LCM) of 113 and 125
The least common multiple (LCM) of 113 and 125 is 14125.
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 125?
First, calculate the GCD of 113 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 125 = 0 remainder 113 |
| 2 | 125 ÷ 113 = 1 remainder 12 |
| 3 | 113 ÷ 12 = 9 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 97 | 4753 |
| 47 and 175 | 8225 |
| 137 and 194 | 26578 |
| 20 and 96 | 480 |
| 133 and 74 | 9842 |