Least Common Multiple (LCM) of 100 and 182
The least common multiple (LCM) of 100 and 182 is 9100.
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 182?
First, calculate the GCD of 100 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 182 = 0 remainder 100 |
| 2 | 182 ÷ 100 = 1 remainder 82 |
| 3 | 100 ÷ 82 = 1 remainder 18 |
| 4 | 82 ÷ 18 = 4 remainder 10 |
| 5 | 18 ÷ 10 = 1 remainder 8 |
| 6 | 10 ÷ 8 = 1 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 28 | 2380 |
| 26 and 131 | 3406 |
| 135 and 25 | 675 |
| 111 and 83 | 9213 |
| 143 and 71 | 10153 |