Least Common Multiple (LCM) of 107 and 180
The least common multiple (LCM) of 107 and 180 is 19260.
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 180?
First, calculate the GCD of 107 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 180 = 0 remainder 107 |
| 2 | 180 ÷ 107 = 1 remainder 73 |
| 3 | 107 ÷ 73 = 1 remainder 34 |
| 4 | 73 ÷ 34 = 2 remainder 5 |
| 5 | 34 ÷ 5 = 6 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 73 | 4672 |
| 154 and 31 | 4774 |
| 114 and 65 | 7410 |
| 14 and 21 | 42 |
| 145 and 30 | 870 |