Least Common Multiple (LCM) of 73 and 137
The least common multiple (LCM) of 73 and 137 is 10001.
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 73 and 137?
First, calculate the GCD of 73 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 137 = 0 remainder 73 |
| 2 | 137 ÷ 73 = 1 remainder 64 |
| 3 | 73 ÷ 64 = 1 remainder 9 |
| 4 | 64 ÷ 9 = 7 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 70 | 560 |
| 45 and 37 | 1665 |
| 73 and 14 | 1022 |
| 51 and 140 | 7140 |
| 104 and 195 | 1560 |