Least Common Multiple (LCM) of 178 and 191
The least common multiple (LCM) of 178 and 191 is 33998.
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 191?
First, calculate the GCD of 178 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 191 = 0 remainder 178 |
| 2 | 191 ÷ 178 = 1 remainder 13 |
| 3 | 178 ÷ 13 = 13 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 15 | 510 |
| 54 and 17 | 918 |
| 143 and 87 | 12441 |
| 108 and 182 | 9828 |
| 193 and 42 | 8106 |