Least Common Multiple (LCM) of 127 and 72
The least common multiple (LCM) of 127 and 72 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 127 and 72?
First, calculate the GCD of 127 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 72 = 1 remainder 55 |
| 2 | 72 ÷ 55 = 1 remainder 17 |
| 3 | 55 ÷ 17 = 3 remainder 4 |
| 4 | 17 ÷ 4 = 4 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 144 | 1872 |
| 99 and 138 | 4554 |
| 43 and 138 | 5934 |
| 133 and 190 | 1330 |
| 87 and 13 | 1131 |