Least Common Multiple (LCM) of 107 and 140
The least common multiple (LCM) of 107 and 140 is 14980.
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 140?
First, calculate the GCD of 107 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 140 = 0 remainder 107 |
| 2 | 140 ÷ 107 = 1 remainder 33 |
| 3 | 107 ÷ 33 = 3 remainder 8 |
| 4 | 33 ÷ 8 = 4 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 114 | 1938 |
| 174 and 120 | 3480 |
| 13 and 176 | 2288 |
| 81 and 63 | 567 |
| 16 and 171 | 2736 |