Least Common Multiple (LCM) of 111 and 160
The least common multiple (LCM) of 111 and 160 is 17760.
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 111 and 160?
First, calculate the GCD of 111 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 160 = 0 remainder 111 |
| 2 | 160 ÷ 111 = 1 remainder 49 |
| 3 | 111 ÷ 49 = 2 remainder 13 |
| 4 | 49 ÷ 13 = 3 remainder 10 |
| 5 | 13 ÷ 10 = 1 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 58 | 2610 |
| 37 and 137 | 5069 |
| 139 and 101 | 14039 |
| 45 and 77 | 3465 |
| 19 and 126 | 2394 |