Least Common Multiple (LCM) of 170 and 71
The least common multiple (LCM) of 170 and 71 is 12070.
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 71?
First, calculate the GCD of 170 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 71 = 2 remainder 28 |
| 2 | 71 ÷ 28 = 2 remainder 15 |
| 3 | 28 ÷ 15 = 1 remainder 13 |
| 4 | 15 ÷ 13 = 1 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 29 | 3973 |
| 147 and 31 | 4557 |
| 98 and 117 | 11466 |
| 145 and 35 | 1015 |
| 94 and 194 | 9118 |