Least Common Multiple (LCM) of 172 and 178
The least common multiple (LCM) of 172 and 178 is 15308.
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 172 and 178?
First, calculate the GCD of 172 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 178 = 0 remainder 172 |
| 2 | 178 ÷ 172 = 1 remainder 6 |
| 3 | 172 ÷ 6 = 28 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 63 | 1134 |
| 74 and 54 | 1998 |
| 180 and 114 | 3420 |
| 40 and 62 | 1240 |
| 82 and 184 | 7544 |