Least Common Multiple (LCM) of 100 and 143
The least common multiple (LCM) of 100 and 143 is 14300.
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 143?
First, calculate the GCD of 100 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 143 = 0 remainder 100 |
| 2 | 143 ÷ 100 = 1 remainder 43 |
| 3 | 100 ÷ 43 = 2 remainder 14 |
| 4 | 43 ÷ 14 = 3 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 64 | 192 |
| 95 and 102 | 9690 |
| 86 and 67 | 5762 |
| 15 and 95 | 285 |
| 126 and 165 | 6930 |