Least Common Multiple (LCM) of 112 and 164
The least common multiple (LCM) of 112 and 164 is 4592.
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 164?
First, calculate the GCD of 112 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 164 = 0 remainder 112 |
| 2 | 164 ÷ 112 = 1 remainder 52 |
| 3 | 112 ÷ 52 = 2 remainder 8 |
| 4 | 52 ÷ 8 = 6 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 175 | 2800 |
| 68 and 56 | 952 |
| 20 and 99 | 1980 |
| 161 and 47 | 7567 |
| 56 and 200 | 1400 |