Least Common Multiple (LCM) of 70 and 171
The least common multiple (LCM) of 70 and 171 is 11970.
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 70 and 171?
First, calculate the GCD of 70 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 171 = 0 remainder 70 |
| 2 | 171 ÷ 70 = 2 remainder 31 |
| 3 | 70 ÷ 31 = 2 remainder 8 |
| 4 | 31 ÷ 8 = 3 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 42 | 756 |
| 197 and 145 | 28565 |
| 195 and 33 | 2145 |
| 47 and 115 | 5405 |
| 191 and 102 | 19482 |