Least Common Multiple (LCM) of 167 and 128
The least common multiple (LCM) of 167 and 128 is 21376.
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 167 and 128?
First, calculate the GCD of 167 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 128 = 1 remainder 39 |
| 2 | 128 ÷ 39 = 3 remainder 11 |
| 3 | 39 ÷ 11 = 3 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 188 | 564 |
| 16 and 200 | 400 |
| 135 and 131 | 17685 |
| 172 and 58 | 4988 |
| 104 and 46 | 2392 |