Least Common Multiple (LCM) of 114 and 160
The least common multiple (LCM) of 114 and 160 is 9120.
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 114 and 160?
First, calculate the GCD of 114 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 160 = 0 remainder 114 |
| 2 | 160 ÷ 114 = 1 remainder 46 |
| 3 | 114 ÷ 46 = 2 remainder 22 |
| 4 | 46 ÷ 22 = 2 remainder 2 |
| 5 | 22 ÷ 2 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 147 | 735 |
| 16 and 97 | 1552 |
| 34 and 15 | 510 |
| 108 and 31 | 3348 |
| 75 and 66 | 1650 |