Least Common Multiple (LCM) of 138 and 177
The least common multiple (LCM) of 138 and 177 is 8142.
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 177?
First, calculate the GCD of 138 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 177 = 0 remainder 138 |
| 2 | 177 ÷ 138 = 1 remainder 39 |
| 3 | 138 ÷ 39 = 3 remainder 21 |
| 4 | 39 ÷ 21 = 1 remainder 18 |
| 5 | 21 ÷ 18 = 1 remainder 3 |
| 6 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 144 | 15408 |
| 105 and 29 | 3045 |
| 192 and 110 | 10560 |
| 136 and 54 | 3672 |
| 30 and 157 | 4710 |