Least Common Multiple (LCM) of 113 and 167
The least common multiple (LCM) of 113 and 167 is 18871.
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 167?
First, calculate the GCD of 113 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 167 = 0 remainder 113 |
| 2 | 167 ÷ 113 = 1 remainder 54 |
| 3 | 113 ÷ 54 = 2 remainder 5 |
| 4 | 54 ÷ 5 = 10 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 120 | 360 |
| 106 and 104 | 5512 |
| 55 and 55 | 55 |
| 15 and 124 | 1860 |
| 148 and 161 | 23828 |