Least Common Multiple (LCM) of 130 and 171
The least common multiple (LCM) of 130 and 171 is 22230.
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 130 and 171?
First, calculate the GCD of 130 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 171 = 0 remainder 130 |
| 2 | 171 ÷ 130 = 1 remainder 41 |
| 3 | 130 ÷ 41 = 3 remainder 7 |
| 4 | 41 ÷ 7 = 5 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 170 | 9180 |
| 21 and 132 | 924 |
| 134 and 65 | 8710 |
| 147 and 121 | 17787 |
| 16 and 183 | 2928 |