Least Common Multiple (LCM) of 113 and 119
The least common multiple (LCM) of 113 and 119 is 13447.
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 119?
First, calculate the GCD of 113 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 119 = 0 remainder 113 |
| 2 | 119 ÷ 113 = 1 remainder 6 |
| 3 | 113 ÷ 6 = 18 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 30 | 1860 |
| 192 and 110 | 10560 |
| 130 and 22 | 1430 |
| 68 and 60 | 1020 |
| 198 and 116 | 11484 |