Least Common Multiple (LCM) of 84 and 130
The least common multiple (LCM) of 84 and 130 is 5460.
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 84 and 130?
First, calculate the GCD of 84 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 130 = 0 remainder 84 |
| 2 | 130 ÷ 84 = 1 remainder 46 |
| 3 | 84 ÷ 46 = 1 remainder 38 |
| 4 | 46 ÷ 38 = 1 remainder 8 |
| 5 | 38 ÷ 8 = 4 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 93 | 1767 |
| 26 and 16 | 208 |
| 197 and 113 | 22261 |
| 24 and 23 | 552 |
| 15 and 12 | 60 |