Least Common Multiple (LCM) of 128 and 167
The least common multiple (LCM) of 128 and 167 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 128 and 167?
First, calculate the GCD of 128 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 167 = 0 remainder 128 |
| 2 | 167 ÷ 128 = 1 remainder 39 |
| 3 | 128 ÷ 39 = 3 remainder 11 |
| 4 | 39 ÷ 11 = 3 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 169 | 1014 |
| 174 and 161 | 28014 |
| 102 and 89 | 9078 |
| 118 and 48 | 2832 |
| 101 and 106 | 10706 |