Least Common Multiple (LCM) of 130 and 170
The least common multiple (LCM) of 130 and 170 is 2210.
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 170?
First, calculate the GCD of 130 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 170 = 0 remainder 130 |
| 2 | 170 ÷ 130 = 1 remainder 40 |
| 3 | 130 ÷ 40 = 3 remainder 10 |
| 4 | 40 ÷ 10 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 112 | 9968 |
| 88 and 78 | 3432 |
| 172 and 121 | 20812 |
| 60 and 88 | 1320 |
| 128 and 105 | 13440 |