Least Common Multiple (LCM) of 130 and 100
The least common multiple (LCM) of 130 and 100 is 1300.
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 100?
First, calculate the GCD of 130 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 100 = 1 remainder 30 |
| 2 | 100 ÷ 30 = 3 remainder 10 |
| 3 | 30 ÷ 10 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 105 | 3570 |
| 120 and 128 | 1920 |
| 108 and 16 | 432 |
| 23 and 107 | 2461 |
| 114 and 117 | 4446 |