Least Common Multiple (LCM) of 138 and 171
The least common multiple (LCM) of 138 and 171 is 7866.
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 171?
First, calculate the GCD of 138 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 171 = 0 remainder 138 |
| 2 | 171 ÷ 138 = 1 remainder 33 |
| 3 | 138 ÷ 33 = 4 remainder 6 |
| 4 | 33 ÷ 6 = 5 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 98 | 5194 |
| 175 and 169 | 29575 |
| 183 and 129 | 7869 |
| 176 and 167 | 29392 |
| 130 and 65 | 130 |