Least Common Multiple (LCM) of 178 and 141
The least common multiple (LCM) of 178 and 141 is 25098.
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 141?
First, calculate the GCD of 178 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 141 = 1 remainder 37 |
| 2 | 141 ÷ 37 = 3 remainder 30 |
| 3 | 37 ÷ 30 = 1 remainder 7 |
| 4 | 30 ÷ 7 = 4 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 121 | 5808 |
| 144 and 132 | 1584 |
| 131 and 105 | 13755 |
| 165 and 126 | 6930 |
| 173 and 155 | 26815 |