Least Common Multiple (LCM) of 138 and 172
The least common multiple (LCM) of 138 and 172 is 11868.
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 172?
First, calculate the GCD of 138 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 172 = 0 remainder 138 |
| 2 | 172 ÷ 138 = 1 remainder 34 |
| 3 | 138 ÷ 34 = 4 remainder 2 |
| 4 | 34 ÷ 2 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 107 | 16585 |
| 120 and 78 | 1560 |
| 10 and 88 | 440 |
| 164 and 23 | 3772 |
| 147 and 94 | 13818 |