Least Common Multiple (LCM) of 68 and 130
The least common multiple (LCM) of 68 and 130 is 4420.
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 68 and 130?
First, calculate the GCD of 68 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 130 = 0 remainder 68 |
| 2 | 130 ÷ 68 = 1 remainder 62 |
| 3 | 68 ÷ 62 = 1 remainder 6 |
| 4 | 62 ÷ 6 = 10 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 128 | 9088 |
| 139 and 126 | 17514 |
| 180 and 52 | 2340 |
| 47 and 138 | 6486 |
| 36 and 127 | 4572 |