Least Common Multiple (LCM) of 113 and 158
The least common multiple (LCM) of 113 and 158 is 17854.
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 158?
First, calculate the GCD of 113 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 158 = 0 remainder 113 |
| 2 | 158 ÷ 113 = 1 remainder 45 |
| 3 | 113 ÷ 45 = 2 remainder 23 |
| 4 | 45 ÷ 23 = 1 remainder 22 |
| 5 | 23 ÷ 22 = 1 remainder 1 |
| 6 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 151 | 30049 |
| 67 and 85 | 5695 |
| 51 and 123 | 2091 |
| 70 and 81 | 5670 |
| 52 and 107 | 5564 |