Least Common Multiple (LCM) of 34 and 130
The least common multiple (LCM) of 34 and 130 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 34 and 130?
First, calculate the GCD of 34 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 130 = 0 remainder 34 |
| 2 | 130 ÷ 34 = 3 remainder 28 |
| 3 | 34 ÷ 28 = 1 remainder 6 |
| 4 | 28 ÷ 6 = 4 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 87 | 5742 |
| 123 and 100 | 12300 |
| 59 and 89 | 5251 |
| 15 and 125 | 375 |
| 161 and 94 | 15134 |