Least Common Multiple (LCM) of 72 and 137
The least common multiple (LCM) of 72 and 137 is 9864.
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 137?
First, calculate the GCD of 72 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 137 = 0 remainder 72 |
| 2 | 137 ÷ 72 = 1 remainder 65 |
| 3 | 72 ÷ 65 = 1 remainder 7 |
| 4 | 65 ÷ 7 = 9 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 97 | 7566 |
| 50 and 29 | 1450 |
| 107 and 156 | 16692 |
| 28 and 47 | 1316 |
| 104 and 101 | 10504 |