Least Common Multiple (LCM) of 128 and 172
The least common multiple (LCM) of 128 and 172 is 5504.
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 172?
First, calculate the GCD of 128 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 172 = 0 remainder 128 |
| 2 | 172 ÷ 128 = 1 remainder 44 |
| 3 | 128 ÷ 44 = 2 remainder 40 |
| 4 | 44 ÷ 40 = 1 remainder 4 |
| 5 | 40 ÷ 4 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 83 | 8881 |
| 129 and 106 | 13674 |
| 30 and 141 | 1410 |
| 127 and 160 | 20320 |
| 112 and 100 | 2800 |