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 |
|---|---|
| 123 and 180 | 7380 |
| 120 and 148 | 4440 |
| 184 and 140 | 6440 |
| 142 and 123 | 17466 |
| 192 and 60 | 960 |