Least Common Multiple (LCM) of 178 and 199
The least common multiple (LCM) of 178 and 199 is 35422.
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 199?
First, calculate the GCD of 178 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 199 = 0 remainder 178 |
| 2 | 199 ÷ 178 = 1 remainder 21 |
| 3 | 178 ÷ 21 = 8 remainder 10 |
| 4 | 21 ÷ 10 = 2 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 77 | 4004 |
| 132 and 107 | 14124 |
| 125 and 39 | 4875 |
| 64 and 130 | 4160 |
| 56 and 40 | 280 |