Least Common Multiple (LCM) of 107 and 135
The least common multiple (LCM) of 107 and 135 is 14445.
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 135?
First, calculate the GCD of 107 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 135 = 0 remainder 107 |
| 2 | 135 ÷ 107 = 1 remainder 28 |
| 3 | 107 ÷ 28 = 3 remainder 23 |
| 4 | 28 ÷ 23 = 1 remainder 5 |
| 5 | 23 ÷ 5 = 4 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 91 | 364 |
| 12 and 75 | 300 |
| 113 and 20 | 2260 |
| 132 and 151 | 19932 |
| 91 and 20 | 1820 |