Least Common Multiple (LCM) of 73 and 178
The least common multiple (LCM) of 73 and 178 is 12994.
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 178?
First, calculate the GCD of 73 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 178 = 0 remainder 73 |
| 2 | 178 ÷ 73 = 2 remainder 32 |
| 3 | 73 ÷ 32 = 2 remainder 9 |
| 4 | 32 ÷ 9 = 3 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 85 | 2465 |
| 200 and 185 | 7400 |
| 83 and 103 | 8549 |
| 137 and 108 | 14796 |
| 114 and 64 | 3648 |