Least Common Multiple (LCM) of 170 and 101
The least common multiple (LCM) of 170 and 101 is 17170.
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 101?
First, calculate the GCD of 170 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 101 = 1 remainder 69 |
| 2 | 101 ÷ 69 = 1 remainder 32 |
| 3 | 69 ÷ 32 = 2 remainder 5 |
| 4 | 32 ÷ 5 = 6 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 50 | 850 |
| 176 and 122 | 10736 |
| 174 and 66 | 1914 |
| 76 and 112 | 2128 |
| 198 and 66 | 198 |