Least Common Multiple (LCM) of 178 and 73
The least common multiple (LCM) of 178 and 73 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 178 and 73?
First, calculate the GCD of 178 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 73 = 2 remainder 32 |
| 2 | 73 ÷ 32 = 2 remainder 9 |
| 3 | 32 ÷ 9 = 3 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 37 | 6919 |
| 123 and 179 | 22017 |
| 24 and 100 | 600 |
| 13 and 90 | 1170 |
| 136 and 87 | 11832 |