Least Common Multiple (LCM) of 40 and 127
The least common multiple (LCM) of 40 and 127 is 5080.
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 40 and 127?
First, calculate the GCD of 40 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 127 = 0 remainder 40 |
| 2 | 127 ÷ 40 = 3 remainder 7 |
| 3 | 40 ÷ 7 = 5 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 128 | 23680 |
| 160 and 27 | 4320 |
| 79 and 98 | 7742 |
| 29 and 115 | 3335 |
| 200 and 144 | 3600 |