Least Common Multiple (LCM) of 21 and 130
The least common multiple (LCM) of 21 and 130 is 2730.
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 21 and 130?
First, calculate the GCD of 21 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 130 = 0 remainder 21 |
| 2 | 130 ÷ 21 = 6 remainder 4 |
| 3 | 21 ÷ 4 = 5 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 21 | 2310 |
| 50 and 106 | 2650 |
| 21 and 88 | 1848 |
| 57 and 29 | 1653 |
| 200 and 78 | 7800 |