Least Common Multiple (LCM) of 113 and 73
The least common multiple (LCM) of 113 and 73 is 8249.
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 113 and 73?
First, calculate the GCD of 113 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 73 = 1 remainder 40 |
| 2 | 73 ÷ 40 = 1 remainder 33 |
| 3 | 40 ÷ 33 = 1 remainder 7 |
| 4 | 33 ÷ 7 = 4 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 56 | 7784 |
| 138 and 165 | 7590 |
| 133 and 164 | 21812 |
| 183 and 150 | 9150 |
| 33 and 81 | 891 |