Least Common Multiple (LCM) of 96 and 172
The least common multiple (LCM) of 96 and 172 is 4128.
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 96 and 172?
First, calculate the GCD of 96 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 172 = 0 remainder 96 |
| 2 | 172 ÷ 96 = 1 remainder 76 |
| 3 | 96 ÷ 76 = 1 remainder 20 |
| 4 | 76 ÷ 20 = 3 remainder 16 |
| 5 | 20 ÷ 16 = 1 remainder 4 |
| 6 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 108 | 6588 |
| 174 and 113 | 19662 |
| 54 and 125 | 6750 |
| 59 and 113 | 6667 |
| 176 and 173 | 30448 |