Least Common Multiple (LCM) of 100 and 160
The least common multiple (LCM) of 100 and 160 is 800.
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 100 and 160?
First, calculate the GCD of 100 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 160 = 0 remainder 100 |
| 2 | 160 ÷ 100 = 1 remainder 60 |
| 3 | 100 ÷ 60 = 1 remainder 40 |
| 4 | 60 ÷ 40 = 1 remainder 20 |
| 5 | 40 ÷ 20 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 134 | 804 |
| 186 and 12 | 372 |
| 53 and 177 | 9381 |
| 14 and 117 | 1638 |
| 48 and 54 | 432 |