Least Common Multiple (LCM) of 100 and 146
The least common multiple (LCM) of 100 and 146 is 7300.
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 146?
First, calculate the GCD of 100 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 146 = 0 remainder 100 |
| 2 | 146 ÷ 100 = 1 remainder 46 |
| 3 | 100 ÷ 46 = 2 remainder 8 |
| 4 | 46 ÷ 8 = 5 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 33 | 297 |
| 132 and 125 | 16500 |
| 84 and 187 | 15708 |
| 110 and 134 | 7370 |
| 50 and 63 | 3150 |