Least Common Multiple (LCM) of 127 and 45
The least common multiple (LCM) of 127 and 45 is 5715.
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 45?
First, calculate the GCD of 127 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 45 = 2 remainder 37 |
| 2 | 45 ÷ 37 = 1 remainder 8 |
| 3 | 37 ÷ 8 = 4 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 110 | 14190 |
| 113 and 198 | 22374 |
| 107 and 56 | 5992 |
| 169 and 155 | 26195 |
| 88 and 84 | 1848 |