Least Common Multiple (LCM) of 170 and 196
The least common multiple (LCM) of 170 and 196 is 16660.
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 196?
First, calculate the GCD of 170 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 196 = 0 remainder 170 |
| 2 | 196 ÷ 170 = 1 remainder 26 |
| 3 | 170 ÷ 26 = 6 remainder 14 |
| 4 | 26 ÷ 14 = 1 remainder 12 |
| 5 | 14 ÷ 12 = 1 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 10 | 120 |
| 128 and 47 | 6016 |
| 130 and 124 | 8060 |
| 179 and 27 | 4833 |
| 136 and 171 | 23256 |