Least Common Multiple (LCM) of 72 and 127
The least common multiple (LCM) of 72 and 127 is 9144.
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 72 and 127?
First, calculate the GCD of 72 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 127 = 0 remainder 72 |
| 2 | 127 ÷ 72 = 1 remainder 55 |
| 3 | 72 ÷ 55 = 1 remainder 17 |
| 4 | 55 ÷ 17 = 3 remainder 4 |
| 5 | 17 ÷ 4 = 4 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 98 | 2450 |
| 75 and 128 | 9600 |
| 160 and 183 | 29280 |
| 17 and 200 | 3400 |
| 147 and 156 | 7644 |