Least Common Multiple (LCM) of 101 and 170
The least common multiple (LCM) of 101 and 170 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 101 and 170?
First, calculate the GCD of 101 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 170 = 0 remainder 101 |
| 2 | 170 ÷ 101 = 1 remainder 69 |
| 3 | 101 ÷ 69 = 1 remainder 32 |
| 4 | 69 ÷ 32 = 2 remainder 5 |
| 5 | 32 ÷ 5 = 6 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 120 | 4920 |
| 156 and 77 | 12012 |
| 100 and 194 | 9700 |
| 22 and 200 | 2200 |
| 170 and 136 | 680 |