Least Common Multiple (LCM) of 67 and 130
The least common multiple (LCM) of 67 and 130 is 8710.
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 67 and 130?
First, calculate the GCD of 67 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 130 = 0 remainder 67 |
| 2 | 130 ÷ 67 = 1 remainder 63 |
| 3 | 67 ÷ 63 = 1 remainder 4 |
| 4 | 63 ÷ 4 = 15 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 75 | 3075 |
| 142 and 160 | 11360 |
| 16 and 12 | 48 |
| 179 and 122 | 21838 |
| 90 and 98 | 4410 |