Least Common Multiple (LCM) of 108 and 160
The least common multiple (LCM) of 108 and 160 is 4320.
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 108 and 160?
First, calculate the GCD of 108 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 160 = 0 remainder 108 |
| 2 | 160 ÷ 108 = 1 remainder 52 |
| 3 | 108 ÷ 52 = 2 remainder 4 |
| 4 | 52 ÷ 4 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 30 | 1590 |
| 75 and 167 | 12525 |
| 38 and 133 | 266 |
| 42 and 196 | 588 |
| 106 and 169 | 17914 |