Least Common Multiple (LCM) of 127 and 100
The least common multiple (LCM) of 127 and 100 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 127 and 100?
First, calculate the GCD of 127 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 100 = 1 remainder 27 |
| 2 | 100 ÷ 27 = 3 remainder 19 |
| 3 | 27 ÷ 19 = 1 remainder 8 |
| 4 | 19 ÷ 8 = 2 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 138 | 3036 |
| 44 and 102 | 2244 |
| 155 and 148 | 22940 |
| 186 and 48 | 1488 |
| 45 and 47 | 2115 |