Least Common Multiple (LCM) of 107 and 145
The least common multiple (LCM) of 107 and 145 is 15515.
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 145?
First, calculate the GCD of 107 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 145 = 0 remainder 107 |
| 2 | 145 ÷ 107 = 1 remainder 38 |
| 3 | 107 ÷ 38 = 2 remainder 31 |
| 4 | 38 ÷ 31 = 1 remainder 7 |
| 5 | 31 ÷ 7 = 4 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 200 | 2200 |
| 123 and 73 | 8979 |
| 137 and 146 | 20002 |
| 35 and 15 | 105 |
| 22 and 22 | 22 |