Least Common Multiple (LCM) of 176 and 138
The least common multiple (LCM) of 176 and 138 is 12144.
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 176 and 138?
First, calculate the GCD of 176 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 138 = 1 remainder 38 |
| 2 | 138 ÷ 38 = 3 remainder 24 |
| 3 | 38 ÷ 24 = 1 remainder 14 |
| 4 | 24 ÷ 14 = 1 remainder 10 |
| 5 | 14 ÷ 10 = 1 remainder 4 |
| 6 | 10 ÷ 4 = 2 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 29 | 4321 |
| 97 and 132 | 12804 |
| 191 and 61 | 11651 |
| 148 and 142 | 10508 |
| 130 and 144 | 9360 |