Least Common Multiple (LCM) of 107 and 130
The least common multiple (LCM) of 107 and 130 is 13910.
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 107 and 130?
First, calculate the GCD of 107 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 130 = 0 remainder 107 |
| 2 | 130 ÷ 107 = 1 remainder 23 |
| 3 | 107 ÷ 23 = 4 remainder 15 |
| 4 | 23 ÷ 15 = 1 remainder 8 |
| 5 | 15 ÷ 8 = 1 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 70 | 350 |
| 155 and 196 | 30380 |
| 102 and 50 | 2550 |
| 93 and 62 | 186 |
| 120 and 132 | 1320 |