Least Common Multiple (LCM) of 73 and 133
The least common multiple (LCM) of 73 and 133 is 9709.
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 133?
First, calculate the GCD of 73 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 133 = 0 remainder 73 |
| 2 | 133 ÷ 73 = 1 remainder 60 |
| 3 | 73 ÷ 60 = 1 remainder 13 |
| 4 | 60 ÷ 13 = 4 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 18 | 1440 |
| 57 and 108 | 2052 |
| 183 and 192 | 11712 |
| 25 and 30 | 150 |
| 70 and 110 | 770 |