Least Common Multiple (LCM) of 107 and 148
The least common multiple (LCM) of 107 and 148 is 15836.
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 148?
First, calculate the GCD of 107 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 148 = 0 remainder 107 |
| 2 | 148 ÷ 107 = 1 remainder 41 |
| 3 | 107 ÷ 41 = 2 remainder 25 |
| 4 | 41 ÷ 25 = 1 remainder 16 |
| 5 | 25 ÷ 16 = 1 remainder 9 |
| 6 | 16 ÷ 9 = 1 remainder 7 |
| 7 | 9 ÷ 7 = 1 remainder 2 |
| 8 | 7 ÷ 2 = 3 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 86 | 3870 |
| 77 and 114 | 8778 |
| 195 and 126 | 8190 |
| 10 and 199 | 1990 |
| 66 and 82 | 2706 |