Least Common Multiple (LCM) of 100 and 130
The least common multiple (LCM) of 100 and 130 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 100 and 130?
First, calculate the GCD of 100 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 130 = 0 remainder 100 |
| 2 | 130 ÷ 100 = 1 remainder 30 |
| 3 | 100 ÷ 30 = 3 remainder 10 |
| 4 | 30 ÷ 10 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 26 and 165 | 4290 |
| 15 and 38 | 570 |
| 135 and 154 | 20790 |
| 39 and 138 | 1794 |
| 68 and 184 | 3128 |