Least Common Multiple (LCM) of 138 and 176
The least common multiple (LCM) of 138 and 176 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 138 and 176?
First, calculate the GCD of 138 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 176 = 0 remainder 138 |
| 2 | 176 ÷ 138 = 1 remainder 38 |
| 3 | 138 ÷ 38 = 3 remainder 24 |
| 4 | 38 ÷ 24 = 1 remainder 14 |
| 5 | 24 ÷ 14 = 1 remainder 10 |
| 6 | 14 ÷ 10 = 1 remainder 4 |
| 7 | 10 ÷ 4 = 2 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 96 | 1056 |
| 58 and 177 | 10266 |
| 179 and 110 | 19690 |
| 164 and 26 | 2132 |
| 23 and 74 | 1702 |