Least Common Multiple (LCM) of 170 and 96
The least common multiple (LCM) of 170 and 96 is 8160.
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 170 and 96?
First, calculate the GCD of 170 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 96 = 1 remainder 74 |
| 2 | 96 ÷ 74 = 1 remainder 22 |
| 3 | 74 ÷ 22 = 3 remainder 8 |
| 4 | 22 ÷ 8 = 2 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 115 | 3795 |
| 41 and 130 | 5330 |
| 54 and 85 | 4590 |
| 136 and 32 | 544 |
| 131 and 14 | 1834 |