Least Common Multiple (LCM) of 113 and 107
The least common multiple (LCM) of 113 and 107 is 12091.
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 107?
First, calculate the GCD of 113 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 107 = 1 remainder 6 |
| 2 | 107 ÷ 6 = 17 remainder 5 |
| 3 | 6 ÷ 5 = 1 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 151 | 11023 |
| 110 and 164 | 9020 |
| 13 and 113 | 1469 |
| 124 and 126 | 7812 |
| 172 and 111 | 19092 |