Least Common Multiple (LCM) of 100 and 127
The least common multiple (LCM) of 100 and 127 is 12700.
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 127?
First, calculate the GCD of 100 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 127 = 0 remainder 100 |
| 2 | 127 ÷ 100 = 1 remainder 27 |
| 3 | 100 ÷ 27 = 3 remainder 19 |
| 4 | 27 ÷ 19 = 1 remainder 8 |
| 5 | 19 ÷ 8 = 2 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 112 | 11312 |
| 61 and 49 | 2989 |
| 137 and 133 | 18221 |
| 77 and 44 | 308 |
| 17 and 110 | 1870 |