Least Common Multiple (LCM) of 118 and 73
The least common multiple (LCM) of 118 and 73 is 8614.
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 118 and 73?
First, calculate the GCD of 118 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 73 = 1 remainder 45 |
| 2 | 73 ÷ 45 = 1 remainder 28 |
| 3 | 45 ÷ 28 = 1 remainder 17 |
| 4 | 28 ÷ 17 = 1 remainder 11 |
| 5 | 17 ÷ 11 = 1 remainder 6 |
| 6 | 11 ÷ 6 = 1 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 106 | 14098 |
| 85 and 144 | 12240 |
| 48 and 102 | 816 |
| 155 and 181 | 28055 |
| 76 and 87 | 6612 |