Least Common Multiple (LCM) of 185 and 138
The least common multiple (LCM) of 185 and 138 is 25530.
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 185 and 138?
First, calculate the GCD of 185 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 138 = 1 remainder 47 |
| 2 | 138 ÷ 47 = 2 remainder 44 |
| 3 | 47 ÷ 44 = 1 remainder 3 |
| 4 | 44 ÷ 3 = 14 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 148 | 5180 |
| 100 and 141 | 14100 |
| 53 and 128 | 6784 |
| 111 and 10 | 1110 |
| 24 and 102 | 408 |