Least Common Multiple (LCM) of 112 and 167
The least common multiple (LCM) of 112 and 167 is 18704.
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 112 and 167?
First, calculate the GCD of 112 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 167 = 0 remainder 112 |
| 2 | 167 ÷ 112 = 1 remainder 55 |
| 3 | 112 ÷ 55 = 2 remainder 2 |
| 4 | 55 ÷ 2 = 27 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 165 | 10560 |
| 83 and 125 | 10375 |
| 86 and 27 | 2322 |
| 123 and 45 | 1845 |
| 50 and 25 | 50 |