Least Common Multiple (LCM) of 107 and 159
The least common multiple (LCM) of 107 and 159 is 17013.
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 159?
First, calculate the GCD of 107 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 159 = 0 remainder 107 |
| 2 | 159 ÷ 107 = 1 remainder 52 |
| 3 | 107 ÷ 52 = 2 remainder 3 |
| 4 | 52 ÷ 3 = 17 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 136 | 10472 |
| 153 and 126 | 2142 |
| 175 and 62 | 10850 |
| 115 and 101 | 11615 |
| 144 and 160 | 1440 |