Least Common Multiple (LCM) of 103 and 160
The least common multiple (LCM) of 103 and 160 is 16480.
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 103 and 160?
First, calculate the GCD of 103 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 160 = 0 remainder 103 |
| 2 | 160 ÷ 103 = 1 remainder 57 |
| 3 | 103 ÷ 57 = 1 remainder 46 |
| 4 | 57 ÷ 46 = 1 remainder 11 |
| 5 | 46 ÷ 11 = 4 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 59 | 5782 |
| 108 and 52 | 1404 |
| 50 and 52 | 1300 |
| 35 and 119 | 595 |
| 107 and 160 | 17120 |